Let $$y^{\prime}=A\,y+g$$
Where $A$ is some $3$ by $3$ matrix and $g$ is $3$ dimensional vector and $-\infty<t<\infty$. I know how to solve this question if I was given $y(t_0)$.
However in a question I am trying to answer I am not given any initial condition.
I have already found the eigenvalues and eigenvectors of $A$ and solved the homogeneous part. But I don't know how to continue to the non-homogeneous part with no condition given. Is there away around this.
Thanks,