Find the general solution of $$\bar{x}' = \begin{pmatrix} 2 & -5 \\ 1 & -2 \\ \end{pmatrix} \bar{x} + \begin{pmatrix} 0 \\ cost \\ \end{pmatrix}, \: 0<t<\pi$$
I find the general solution to the homogenous equation by finding the eigenvectors to the matrix $$\begin{pmatrix} 2 & -5 \\ 1 & -2 \\ \end{pmatrix} $$ I then want to use the method of undetermined coefficients to find a particular solution. But I'm not getting anywhere with the assumption $$\bar{x} = \bar{a}sin t + \bar{b}cos t$$ Have I assumed the wrong form for the particular solution and if so why is it wrong?