Solve analytically an system of coupled diffrential équation with Matlab

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]

Since the coefficients in B and G are already rounded, I think it doesn't make much sense trying to solve your system analytically.

It's not even possible since you had to determine analytically the eigenvalues of the matrix B. This cannot be done since you had to solve for the roots of a polynomial of order 5.

[Torsten]

@Thomas TJOCK-MBAGA comment moved here:

I have obtained the eigen values and eigen vecteurs of the Matrix B with linear algebra [eigenvectors] function. But i dont know how to continuou

[Torsten]

This already involves numerical computations - so why not integrate your equations numerically ?

But if you like to make things complicated:

https://xchen.math.gatech.edu/teach/ode/NonhomoSys.pdf

[Thomas TJOCK-MBAGA]

On fact this equations are equations of transform potentiel for an original ADVECTION-DISPERSION EQUATION. So i wanted to obtain the analytical expressions in order to remplace them in the original analytical solution of the ADE problem.

[Torsten]

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.

Answer 1

[Sam Chak]

@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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