MATLAB: How to solve a system of n differential equations

differential equations

Hello everyone, I got the solution below from the help, I tried an example with a 3×3 system and it runs ok. However, when I try to apply it to my real system, I can not find an answer. Do you have any idea why?
Example:
syms x(t) y(t)
A = [1 2; -1 1];
B = [1; 1];
Y = [x; y];
odes = diff(Y) == A*Y + B;
C = Y(0) == [2; -1];
[xSol(t), ySol(t)] = dsolve(odes,C);
My problem:
clear; close 'all'; clc;
syms T1(t) T2(t) T3(t) T4(t) T5(t) 
syms x(t) y(t) z(t) w(t) p(t)
A = [-81 1 0 0 0
  0.5 -0.56 0.02 0.04 0
  0 0.004 -0.008 0.004 0
  0 0.267 0.13 -1.4 1
  0 0 0.273 3 -82.1];
B = [24000;0;0;1.333;6300];
Y = [x; y; z; w; p];
odes = diff(Y) == A*Y + B;
C = Y(0) == [300; 300; 300; 300; 300];
[xSol(t), ySol(t), zSol(t), wSol(t), pSol(t)] = dsolve(odes,C);

Best Answer

You appear to have a dynamic system. The Control System Toolbox would be more appropriate.
One way to solve it would be to convert it to an anonymous function and solve it with ode45:
[VF,Subs] = odeToVectorField(odes)
Sys = matlabFunction(VF,'Vars',{'t','Y'})
Y0 = [300; 300; 300; 300; 300];
[T,Y] = ode45(Sys, [0 5], Y0);
figure(1)
plot(T,Y)
grid
lgnd = regexp(sprintf('%s\n',Subs), '\n', 'split');
legend(lgnd(1:end-1), 'Location','E')
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