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I have a strange results solving this problem.

x'=[3,4;-1,-1]*x+[e^t;0], with init. cond. x(0)=[1;0].

x'=Ax+(e^(mu*t))*b thus mu=1, b=[1;0]

x(t)=(e^(mu*t))((mu*I-A)^-1)*b

x(t)=e^t*(([mu,0;0,mu]-[3,4;-1,-1])^-1)*b=e^t*([-2,-4;1,2]^-1)*[1;0]

But the problem is that [-2,-4;1,2]^-1 matrix is singular to working precision.

ans =

Inf Inf

Inf Inf

Is that some typo in the matrix or am I using the wrong way to solve this type of equations?

Thank you very much for any ideas!

Best regards,

Alina