Solving System differential equation

Hi, I am new to matlab. I have a very simple question. How can I solve the following differential equation dx/dt = [1,2;3,4]*[x1;x2]+[0;1]?

Thank you very much.

[MoHizzel]

How can I modify this so the answer is a general equation of x in terms of t? So something like x(t)=5e^t[1;1]

[Torsten]

help dsolve

Best wishes

Torsten.

Answer 1

[Sadra]

you could solve it with ODE45

your function is:

function dy = my_ODE(t,y)
    dy=zeros(2,1);
    dy=[1 2;3 4]*[y(1);y(2)]+[0;1];
end

and you should solve it with ODE45 with this script :

Time=2; %2seconds
InitialValues=[0;0];
[t,y]=ode45(@my_ODE,[0 Time],InitialValues)
plot(t,y(1),'-',t,y(2),'-.')
legend('y(1)','y(2)')

[MoHizzel]

Thank you. How can I modify this so the answer is a general equation of x in terms of t? So something like x(t)=5e^t[1;1]

[Star Strider]

Also see the documentation for the matrix exponential, expm.

[Sadra]

you should write your equations in state space ( Y_dot=f(x,t) ) form.

for extra details and exapmle see the documaentation for ODE