Differential equations on MATLAB

I have this exercise but I'm stock:

A =[5 1 0 0; 1 5 0 0; 0 0 1 -2; 0 0 2 1]

a)solve dx/dt = Ax using the differential equation solving commands of MATLAB b) calculate e^(At) c) put the four LI solutions in a 4 x 4 matrix of functions X and solve e^(At)B=X for B

I know if it possible to find the eigenvectors and eigenvalues and the solve for c (the coefficients) but I don;t know if this would be using the differenctial equation solving commands of MATLAB.

Answer 1

[Ryan G]

I believe ODE45 may be what you're looking for. Have a look at that documentation, give it a shot and then if you get stuck you can ask a new question.

I will give you 1 hint, you want to breakup the matrix into a system of equations:

x1' = 5*x1 + x2
x2' = x1 + 5x2' 
etc

and then format it so it works for the solver in MATLAB.

Answer 2

[Azzi Abdelmalek]

function dx=my_eq1(t,x)
dx=zeros(4,1);
A =[5 1 0 0; 1 5 0 0; 0 0 1 -2; 0 0 2 1]
dx=A*x

%call your function

xinitial=[1 1 -1 2];
[t,y]=ode45(@my_eq1, [0 10],xinitial)