How to solve a system of n differential equations?

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Marlon Saveri Silva
评论： Walter Roberson 2018-3-31
Hello everyone, I got the solution below from the help, I tried an example with a 3x3 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);
  2 个评论
Walter Roberson
Walter Roberson 2018-3-31
R2018a finds a solution. It does, however, depend upon an arbitrary constant of integration, which would tend to suggest that dsolve thinks there should be one more initial condition.
Marlon Saveri Silva
Marlon Saveri Silva 2018-3-31
Thanks Walter. I'll check monday if it may be updated to R2018a. Meanwhile, how to edit such constant of integration or do any other think to solve the problem?

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Star Strider
Star Strider 2018-3-31
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')
  5 个评论
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Star Strider
Star Strider 2018-3-31
Not that I’m aware of.
You can try something like this, although you would then have to manually copy the output and paste it to your syms call (without the single quotes):
TV = sprintf('T%d(t) ', 1:10)
TV =
'T1(t) T2(t) T3(t) T4(t) T5(t) T6(t) T7(t) T8(t) T9(t) T10(t) '
I know of no way to do it programmatically.

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