how to solve and plot system of differential equations with extra functions of time build-in

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Malgorzata Wieteska
Malgorzata Wieteska on 31 May 2016
Edited: Star Strider on 31 May 2016
b=0.004; %L/day
c1=0.0058; %(L/ug)/day
c2=0.048; %1/day
alpha=0.7736; %dimensionless
c2=0.048; %1/day
c3=0.004; %1/day
c4=0.061; %1/day
beta1=0.1566; %dimensionless
c5=1.2655; %1/day
gamma=0.0202; %dimensionless
d1=0.6715; %1/day
d2=0.7048; %1/day
k1=0.6876; %1/day
k2=0.69; %1/day
k3=0.6891; %1/day
k4=0.7093; %1/day
syms ReF(t)
syms SeF(t)
>> syms PrF(t)
>> syms Ov1(t)
syms Ov2(t)
syms FSH(t) LH(t)
>> syms Lut1(t)
>> syms Lut2(t)
>> syms Lut3(t)
>> syms Lut4(t)
FSH=@(t) 175*exp(-((t-5)^2)/110)+210*exp(-(t-15)^2)+65*exp(-((t-18)^2)/20)+174.85*exp(-((t-36)^2)/121)+205*exp(-(t-46)^2)+65*exp(-((t-49)^2)/20)+175*exp(-((t-67)^2)/130)
LH=@(t) 0.156+24.38*exp(-((t-7)^2)/230)+332.12*exp(-(t-15)^2)+17.24*exp(-((t-18)^2)/35.16)+24.38*exp(-((t-38)^2)/230)+332.12*exp(-(t-46)^2)+17.24*exp(-((t-49)^2)/35.16)+24.38*exp(-((t-69)^2)/230)
eqn1=diff(ReF)==b*FSH+(c1*FSH-c2*LH^alpha)*ReF;
eqn2=diff(SeF)==c2*(LH^alpha)*ReF+[c3*(LH^beta1)-c4*LH]*SeF;
eqn3=diff(PrF)==c4*LH*SeF-c5*(LH^gamma)*PrF;
eqn4=diff(Ov1)==c5*(LH^gamma)*PrF-d1*Ov1;
eqn5=diff(Ov2)==d1*Ov1-d2*Ov2;
eqn6=diff(Lut1)==d2*Ov2-k1*Lut1;
eqn7=diff(Lut2)==k1*Lut1-k2*Lut2;
eqn8=diff(Lut3)==k2*Lut2-k3*Lut3;
eqn9=diff(Lut4)==k3*Lut3-k4*Lut4;
S=dsolve(eqn1,eqn2,eqn3,eqn4,eqn5,eqn6,eqn7,eqn8,eqn9)
ReFsol(t)=S.ReF
SeFsol(t)=S.SeF
PrFsol(t)=S.PrF
Ov1sol(t)=S.Ov1
Ov2sol(t)=S.Ov2
Lut1sol(t)=S.Lut1
Lut2sol(t)=S.Lut2
Lut3sol(t)=S.Lut3
Lut4sol(t)=S.Lut4
ReFsol(t) =
exp(int((29*FSH(t))/5000 - (6*LH(t)^(967/1250))/125, t))*int((exp(-int((29*FSH(t))/5000 - (6*LH(t)^(967/1250))/125, t))*FSH(t))/250, t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + C1*exp(int((29*FSH(t))/5000 - (6*LH(t)^(967/1250))/125, t))
SeFsol(t) =
exp(int(LH(t)^(783/5000)/250 - (61*LH(t))/1000, t))*int((3*exp(-int(LH(t)^(783/5000)/250 - (61*LH(t))/1000, t))*exp(-(6*int(LH(t)^(967/1250), t))/125)*(250*C1*exp((29*int(FSH(t), t))/5000)*LH(t)^(967/1250) + exp((29*int(FSH(t), t))/5000)*LH(t)^(967/1250)*int(exp(-(29*int(FSH(t), t))/5000)*exp((6*int(LH(t)^(967/1250), t))/125)*FSH(t), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/15625, t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + C2*exp(int(LH(t)^(783/5000)/250 - (61*LH(t))/1000, t))
PrFsol(t) =
exp(int(-(2531*LH(t)^(101/5000))/2000, t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))*int((61*exp(-(61*int(LH(t), t))/1000)*exp(-int(-(2531*LH(t)^(101/5000))/2000, t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))*(15625*C2*exp(int(LH(t)^(783/5000), t)/250)*LH(t) + 3*exp(int(LH(t)^(783/5000), t)/250)*LH(t)*int(exp((29*int(FSH(t), t))/5000)*exp((61*int(LH(t), t))/1000)*exp(-(6*int(LH(t)^(967/1250), t))/125)*exp(-int(LH(t)^(783/5000), t)/250)*LH(t)^(967/1250)*int(exp(-(29*int(FSH(t), t))/5000)*exp((6*int(LH(t)^(967/1250), t))/125)*FSH(t), t), t) + 750*C1*exp(int(LH(t)^(783/5000), t)/250)*LH(t)*int(exp((29*int(FSH(t), t))/5000)*exp((61*int(LH(t), t))/1000)*exp(-(6*int(LH(t)^(967/1250), t))/125)*exp(-int(LH(t)^(783/5000), t)/250)*LH(t)^(967/1250), t)))/15625000, t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + C3*exp(int(-(2531*LH(t)^(101/5000))/2000, t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))
Ov1sol(t) =
(2213673*exp(-(1343*t)/2000)*(C4 + int((1313827744271771*exp((1343*t)/2000)*(183*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000)*int((exp(int(LH(t)^(967/1250), t))^(6/125)*FSH(t))/exp(int(FSH(t), t))^(29/5000), t))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 15625000*C3*LH(t)^(101/5000) + 45750*C1*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 953125*C2*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/(691772812500000*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/51909432804100
Ov2sol(t) =
(19943*exp(-(1343*t)/2000)*(C4 + int((1313827744271771*exp((1343*t)/2000)*(183*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000)*int((exp(int(LH(t)^(967/1250), t))^(6/125)*FSH(t))/exp(int(FSH(t), t))^(29/5000), t))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 15625000*C3*LH(t)^(101/5000) + 45750*C1*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 953125*C2*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/(691772812500000*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/23191109220 - (249787*exp(-(881*t)/1250)*(C6 + int((30218038118250733*exp((881*t)/1250)*(183*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000)*int((exp(int(LH(t)^(967/1250), t))^(6/125)*FSH(t))/exp(int(FSH(t), t))^(29/5000), t))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 15625000*C3*LH(t)^(101/5000) + 45750*C1*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 953125*C2*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/(1444081093750000*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/3200373072360
Lut1sol(t) =
(5698*exp(-(1343*t)/2000)*(C4 + int((1313827744271771*exp((1343*t)/2000)*(183*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000)*int((exp(int(LH(t)^(967/1250), t))^(6/125)*FSH(t))/exp(int(FSH(t), t))^(29/5000), t))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 15625000*C3*LH(t)^(101/5000) + 45750*C1*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 953125*C2*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/(691772812500000*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/151360815 + (5809*exp(-(881*t)/1250)*(C6 + int((30218038118250733*exp((881*t)/1250)*(183*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000)*int((exp(int(LH(t)^(967/1250), t))^(6/125)*FSH(t))/exp(int(FSH(t), t))^(29/5000), t))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 15625000*C3*LH(t)^(101/5000) + 45750*C1*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 953125*C2*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/(1444081093750000*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/1816329780 + (217*exp(-(1719*t)/2500)*(C7 + int(-(11824449698445939*exp((1719*t)/2500)*(183*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000)*int((exp(int(LH(t)^(967/1250), t))^(6/125)*FSH(t))/exp(int(FSH(t), t))^(29/5000), t))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 15625000*C3*LH(t)^(101/5000) + 45750*C1*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 953125*C2*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/(20411562500000*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/908164890
Lut2sol(t) =
(1848*exp(-(1343*t)/2000)*(C4 + int((1313827744271771*exp((1343*t)/2000)*(183*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000)*int((exp(int(LH(t)^(967/1250), t))^(6/125)*FSH(t))/exp(int(FSH(t), t))^(29/5000), t))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 15625000*C3*LH(t)^(101/5000) + 45750*C1*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 953125*C2*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/(691772812500000*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/1320775 - (193*exp(-(69*t)/100)*(C9 + int(-(90654114354752199*exp((69*t)/100)*(183*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000)*int((exp(int(LH(t)^(967/1250), t))^(6/125)*FSH(t))/exp(int(FSH(t), t))^(29/5000), t))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 15625000*C3*LH(t)^(101/5000) + 45750*C1*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 953125*C2*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/(82567812500000*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/5283100 - (157*exp(-(881*t)/1250)*(C6 + int((30218038118250733*exp((881*t)/1250)*(183*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000)*int((exp(int(LH(t)^(967/1250), t))^(6/125)*FSH(t))/exp(int(FSH(t), t))^(29/5000), t))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 15625000*C3*LH(t)^(101/5000) + 45750*C1*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 953125*C2*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/(1444081093750000*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/1056620 + (217*exp(-(1719*t)/2500)*(C7 + int(-(11824449698445939*exp((1719*t)/2500)*(183*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000)*int((exp(int(LH(t)^(967/1250), t))^(6/125)*FSH(t))/exp(int(FSH(t), t))^(29/5000), t))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 15625000*C3*LH(t)^(101/5000) + 45750*C1*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 953125*C2*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/(20411562500000*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/3169860
Lut3sol(t) =
(202*exp(-(6891*t)/10000)*(C5 + int((90654114354752199*exp((6891*t)/10000)*(183*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000)*int((exp(int(LH(t)^(967/1250), t))^(6/125)*FSH(t))/exp(int(FSH(t), t))^(29/5000), t))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 15625000*C3*LH(t)^(101/5000) + 45750*C1*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 953125*C2*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/(54508437500000*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/6891 + (193*exp(-(69*t)/100)*(C9 + int(-(90654114354752199*exp((69*t)/100)*(183*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000)*int((exp(int(LH(t)^(967/1250), t))^(6/125)*FSH(t))/exp(int(FSH(t), t))^(29/5000), t))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 15625000*C3*LH(t)^(101/5000) + 45750*C1*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 953125*C2*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/(82567812500000*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/6891 + (126*exp(-(1343*t)/2000)*(C4 + int((1313827744271771*exp((1343*t)/2000)*(183*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000)*int((exp(int(LH(t)^(967/1250), t))^(6/125)*FSH(t))/exp(int(FSH(t), t))^(29/5000), t))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 15625000*C3*LH(t)^(101/5000) + 45750*C1*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 953125*C2*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/(691772812500000*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/2297 + (15*exp(-(881*t)/1250)*(C6 + int((30218038118250733*exp((881*t)/1250)*(183*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000)*int((exp(int(LH(t)^(967/1250), t))^(6/125)*FSH(t))/exp(int(FSH(t), t))^(29/5000), t))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 15625000*C3*LH(t)^(101/5000) + 45750*C1*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 953125*C2*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/(1444081093750000*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/2297 + (217*exp(-(1719*t)/2500)*(C7 + int(-(11824449698445939*exp((1719*t)/2500)*(183*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000)*int((exp(int(LH(t)^(967/1250), t))^(6/125)*FSH(t))/exp(int(FSH(t), t))^(29/5000), t))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 15625000*C3*LH(t)^(101/5000) + 45750*C1*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 953125*C2*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/(20411562500000*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/6891
Lut4sol(t) =
exp(-(6891*t)/10000)*(C5 + int((90654114354752199*exp((6891*t)/10000)*(183*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000)*int((exp(int(LH(t)^(967/1250), t))^(6/125)*FSH(t))/exp(int(FSH(t), t))^(29/5000), t))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 15625000*C3*LH(t)^(101/5000) + 45750*C1*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 953125*C2*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/(54508437500000*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)) + exp(-(69*t)/100)*(C9 + int(-(90654114354752199*exp((69*t)/100)*(183*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000)*int((exp(int(LH(t)^(967/1250), t))^(6/125)*FSH(t))/exp(int(FSH(t), t))^(29/5000), t))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 15625000*C3*LH(t)^(101/5000) + 45750*C1*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 953125*C2*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/(82567812500000*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)) + exp(-(1343*t)/2000)*(C4 + int((1313827744271771*exp((1343*t)/2000)*(183*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000)*int((exp(int(LH(t)^(967/1250), t))^(6/125)*FSH(t))/exp(int(FSH(t), t))^(29/5000), t))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 15625000*C3*LH(t)^(101/5000) + 45750*C1*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 953125*C2*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/(691772812500000*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)) + exp(-(881*t)/1250)*(C6 + int((30218038118250733*exp((881*t)/1250)*(183*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000)*int((exp(int(LH(t)^(967/1250), t))^(6/125)*FSH(t))/exp(int(FSH(t), t))^(29/5000), t))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 15625000*C3*LH(t)^(101/5000) + 45750*C1*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 953125*C2*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/(1444081093750000*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)) + exp(-(1719*t)/2500)*(C7 + int(-(11824449698445939*exp((1719*t)/2500)*(183*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000)*int((exp(int(LH(t)^(967/1250), t))^(6/125)*FSH(t))/exp(int(FSH(t), t))^(29/5000), t))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 15625000*C3*LH(t)^(101/5000) + 45750*C1*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 953125*C2*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/(20411562500000*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)) + exp(-(7093*t)/10000)*(C8 + int(-(30218038118250733*exp((7093*t)/10000)*(183*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000)*int((exp(int(LH(t)^(967/1250), t))^(6/125)*FSH(t))/exp(int(FSH(t), t))^(29/5000), t))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 15625000*C3*LH(t)^(101/5000) + 45750*C1*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)*int((exp(int(LH(t), t))^(61/1000)*LH(t)^(967/1250)*exp(int(FSH(t), t))^(29/5000))/(exp(int(LH(t)^(967/1250), t))^(6/125)*exp(int(LH(t)^(783/5000), t))^(1/250)), t))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + 953125*C2*LH(t)^(101/5000)*int((exp(int(LH(t)^(783/5000), t))^(1/250)*LH(t)*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000))/exp(int(LH(t), t))^(61/1000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)))/(3469906289062500*exp(int(LH(t)^(101/5000), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))^(2531/2000)), t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true))
% initial conditions
ReF(0)==0
FSH(0)==139.4270;
LH(0)==19.9055;
fplot(ReF)
hold on
fplot(SeF)
fplot(PrF)
fplot(Ov1)
fplot(Ov2)
fplot(Lut1)
fplot(Lut2)
fplot(Lut3)
fplot(Lut4)
grid on
legend('ReF','SeF','PrF','Ov1','Ov2','Lut1','Lut2','Lut3','Lut4','Location','best')
Index exceeds matrix dimensions.
Error in fplot (line 56)
lims = args{2};
I've tried to plot it but without any success. I've tried dde23 9delays are specified in the FSH and LH functions) but I can't figure out. thanks any hint

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