# Is there a better way of solving simultaneous differential

Is there a better way of solving simultaneous differential equations then using dsolve as MATLAB crashes everytime I use it?

So I have a set of simulataneous differential equtions that need to be solved as such:

Ive been using this code but as stated in the title MATLAB crashes is there any better way of doing this:

`clearclcsyms P1(t) P2(t) P3(t) P4(t) P5(t) P6(t) P7(t) P8(t)...    Lam1 Lam2 Lam3 Mu1 Mu2 Mu3% Typing in all the equationseqns = ...   [diff(P1,t) == (-Lam1-Lam2-Lam3)*P1 + (Mu1)*P2 + (Mu2)*P3 + (Mu3)*P4,...    diff(P2,t) == (Lam1)*P1 + (-Mu1-Lam2-Lam3)*P2 + (Mu2)*P5 + (Mu3)*P6,...    diff(P3,t) == (Lam2)*P1 + (-Mu2-Lam1-Lam3)*P3 + (Mu1)*P5 + (Mu3)*P7,...    diff(P4,t) == (Lam3)*P1 + (-Mu3-Lam1-Lam2)*P4 + (Mu1)*P6 + (Mu2)*P7,...    diff(P5,t) == (Lam2)*P2 + (Lam1)*P3 + (-Mu1-Mu2-Lam3)*P5 + (Mu3)*P8,...    diff(P6,t) == (Lam3)*P2 + (Lam1)*P4 + (-Mu1-Mu3-Lam2)*P6 + (Mu2)*P8,...    diff(P7,t) == (Lam3)*P3 + (Lam2)*P4 + (-Mu2-Mu3-Lam1)*P7 + (Mu1)*P8,...    diff(P8,t) == (Lam3)*P5 + (Lam2)*P6 + (Lam1)*P7 + (-Mu1-Mu2-Mu3)*P8]  % Solutions Solversol = dsolve(eqns, P1(0) == 1, P2(0) == 0, P3(0) == 0, P4(0) == 0,P5(0) == 0, P6(0) == 0,...P7(0) == 0, P8(0) == 0)% Printing the SolutionssolP1(t)= sol.P1solP2(t)= sol.P2solP3(t)= sol.P3solP4(t)= sol.P4solP5(t)= sol.P5solP6(t)= sol.P6solP7(t)= sol.P7solP8(t)= sol.P8`

NOTE:-

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You have a linear system:

so the solution is going to be the matrix exponential:

that in MATLAB code is:

`syms P(t) Lam1 Lam2 Lam3 Mu1 Mu2 Mu3 t A = [ - Lam1 - Lam2 - Lam3,                 Mu1,                 Mu2,                 Mu3,                  0,                  0,                  0,                 0                      Lam1, - Lam2 - Lam3 - Mu1,                   0,                   0,                Mu2,                Mu3,                  0,                 0                      Lam2,                   0, - Lam1 - Lam3 - Mu2,                   0,                Mu1,                  0,                Mu3,                 0                      Lam3,                   0,                   0, - Lam1 - Lam2 - Mu3,                  0,                Mu1,                Mu2,                 0                         0,                Lam2,                Lam1,                   0, - Lam3 - Mu1 - Mu2,                  0,                  0,               Mu3                         0,                Lam3,                   0,                Lam1,                  0, - Lam2 - Mu1 - Mu3,                  0,               Mu2                         0,                   0,                Lam3,                Lam2,                  0,                  0, - Lam1 - Mu2 - Mu3,               Mu1                         0,                   0,                   0,                   0,               Lam3,               Lam2,               Lam1, - Mu1 - Mu2 - Mu3];P = expm(A*t)`

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## Technical Source

Simple! That is me, a simple person. I am passionate about knowledge and reading. That’s why I have decided to write and share a bit of my life and thoughts to.