# Solve analytically an system of coupled diffrential équation with Matlab

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Thomas TJOCK-MBAGA on 16 Jun 2022
Edited: Torsten on 16 Jun 2022
I would like to solve analytically the following system of coupled 5 ODES in order one. A(dT/dt)+ B*T = G.I tried to solve it it Maple but an memory error accurs After 30 mins. I dont know how i can solve the system informatique MATLAB in order to obtain analytical expression
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Torsten on 16 Jun 2022
Edited: Torsten on 16 Jun 2022
As I already told you: It is impossible to get analytical expressions because the solution of your ODE system involves solving a polynomial equation of degree 5 which does not have an analytical solution (at least in your case).
But what is the problem ? You can replace the original analytical expressions by a function call and calculate the required results numerically in this function.

Sam Chak on 16 Jun 2022
@Thomas TJOCK-MBAGA, not sure why you want to look for the analytical solution, especially with the given initial condition. Since it is a linear system, you can try using dsolve() to see if it is possible to obtain something like this:
syms v(t) w(t) x(t) y(t) z(t)
eqn1 = diff(v,t) == 0*v + 1*w + 0*x + 0*y + 0*z;
eqn2 = diff(w,t) == 0*v + 0*w + 1*x + 0*y + 0*z;
eqn3 = diff(x,t) == 0*v + 0*w + 0*x + 1*y + 0*z;
eqn4 = diff(y,t) == 0*v + 0*w + 0*x + 0*y + 1*z;
eqn5 = diff(z,t) == -1*v - 5*w - 10*x - 10*y - 5*z + 3*exp(-2*t);
eqns = [eqn1, eqn2, eqn3, eqn4, eqn5];
cond = [v(0)==1, w(0)==0, x(0)==0, y(0)==0, z(0)==0];
Sol = dsolve(eqns, cond)
Sol = struct with fields:
w: exp(-t)*((exp(-t)*(t^4 + 8*t^3 + 24*t^2 + 48*t + 48))/8 - 6) - (t^3*exp(-t)*(3*exp(-t)*(t + 2) - 6))/6 - t*exp(-t)*((exp(-t)*(t^3 + 6*t^2 + 12*t + 12))/2 - 6) + (t^4*exp(-t)*(3*exp(-t) - 4))/24 + (t^2*exp(-t)*((3*exp(-t)*(t + 2)^2)/2 - 6))/2 v: ((exp(-t)*(t^3 + 6*t^2 + 12*t + 12))/2 - 6)*(exp(-t) + t*exp(-t)) - (3*exp(-t) - 4)*(exp(-t) + t*exp(-t) + (t^2*exp(-t))/2 + (t^3*exp(-t))/6 + (t^4*exp(-t))/24) - ((3*exp(-t)*(t + 2)^2)/2 - 6)*(exp(-t) + t*exp(-t) + (t^2*exp(-t))/2) + (3*exp(-t… x: ((3*exp(-t)*(t + 2)^2)/2 - 6)*(t*exp(-t) - (t^2*exp(-t))/2) - ((exp(-t)*(t^3 + 6*t^2 + 12*t + 12))/2 - 6)*(exp(-t) - t*exp(-t)) - ((t^2*exp(-t))/2 - (t^3*exp(-t))/6)*(3*exp(-t)*(t + 2) - 6) + ((t^3*exp(-t))/6 - (t^4*exp(-t))/24)*(3*exp(-t) - 4)… y: (2*exp(-t) - t*exp(-t))*((exp(-t)*(t^3 + 6*t^2 + 12*t + 12))/2 - 6) - (3*exp(-t)*(t + 2) - 6)*(t*exp(-t) - t^2*exp(-t) + (t^3*exp(-t))/6) + ((3*exp(-t)*(t + 2)^2)/2 - 6)*(exp(-t) - 2*t*exp(-t) + (t^2*exp(-t))/2) + (3*exp(-t) - 4)*((t^2*exp(-t))… z: (3*exp(-t) - 4)*(t*exp(-t) - (3*t^2*exp(-t))/2 + (t^3*exp(-t))/2 - (t^4*exp(-t))/24) - (3*exp(-t) - t*exp(-t))*((exp(-t)*(t^3 + 6*t^2 + 12*t + 12))/2 - 6) - (3*exp(-t)*(t + 2) - 6)*(exp(-t) - 3*t*exp(-t) + (3*t^2*exp(-t))/2 - (t^3*exp(-t))/6) -…
Sol.v
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