Question
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: clear clc syms 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 equations eqns = ... [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 Solver sol = 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 Solutions solP1(t)= sol.P1 solP2(t)= sol.P2 solP3(t)= sol.P3 solP4(t)= sol.P4 solP5(t)= sol.P5 solP6(t)= sol.P6 solP7(t)= sol.P7 solP8(t)= sol.P8
Expert Answer
Prashant Kumar
PhD Expert
Answered Aug 20, 2026
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)
My Ryzen 7 1700 machine has been working on this for the past hour and does not appear to be close to finishing. I’m stopping it now, and will let you pursue this.
100% Run Guarantee
3-Hour Fast-Track Delivery
Need a Custom Version or Complete Simulation for This Problem?
Our 500+ PhD engineers build, debug, and optimize working MATLAB scripts and Simulink (.slx) models tailored to your exact assignment rubrics with zero plagiarism.
Tested on MATLAB R2024b / R2026a
Turnitin 0% Plagiarism Report
Free 7-Day Revisions Guarantee
Have a different question? Ask here
Related matlab Questions & Solutions
Browse All →
Explore similar technical troubleshooting questions and verified MATLAB solutions:
Ready-to-Run MATLAB & Simulink Projects
Browse All Projects →