ode 45 formulation of equations in system

Hi,

I believe I have a mistake in the 1st equation of the system but I am unsure how to formulate it correctly then. Could you help?

The original equation I have troubles with is: d/dt (V_sa)= d/dt(Ca*(P1-P_ic))

Out of completion, here are the others:

• d/dt P1 = ( (P_a_b-P1)/(R_la+0.5*R_sa_b) - (P1-P2)/(0.5*R_sa_b+R_sv) )/Ca_b
• d/dt P2= ((P1-P2)/(0.5*R_sa_b+R_sv)-(P2-P_v)/R_lv)/(1/(k_ven*(P2-Pic-Pv1)))
• d/dt xq= ( -xq*Gq( (( (P1-P2)/(0.5*R_sa_b+Rsv) )-q_b)/q_b ) )/tauq
• d/dt xc= (-xc+0.3+0.3*tanh(Pa_co2/Pa_co2_b -1.1))/tau_co2
• d2/dt xm= (eps*u-tau2*(d/dt xm)-xm)/tau1^2

I'm insecure about the 1st (V_sa), the rest should be fine. It'd be great if you could help!

This is the code: (All variables in the eq have been declared before but I won't report them here cause it's unnecessary)

F = @(t, sth) [ Ca_b*(sth(2)-P_ic);
                            ((P_a_b-sth(2))/(R_la + 0.5 *R_sa_b) - (sth(2)-sth(3))/(0.5 *R_sa_b+R_sv))/Ca_b;
                                     ((sth(2)-sth(3))/(0.5 *R_sa_b +R_sv)-(sth(3)-P_v)/R_lv)/ 
                                          1/(k_ven*(sth(3)-P_ic-P_v1)) ;
                                     (-sth(4)+G_q*(( (sth(2)- sth(3))/(0.5 *R_sa_b + R_sv) ) -q_b )/q_b )/tau_q ;
                    (-sth(5) +0.3+3*tanh(Pa_co2/Pa_co2_b -1.1))/tau_co2;
                       sth(7);
                       (eps*u-tau2*sth(7)-sth(6))/tau1^2  ];
 [t, sth] = ode45(F, [0 100], [0 0 0 0 0 0 0]);

V_sa = sth(:,1);
P1 = sth(:,2);
P2 = sth(:,3);
xq= sth(:,4);
xc= sth(:,5);
xm= sth(:,6);
xm1= sth(:,7);