Find a fundamental matrix for the following system $y'(t)=Ay(t)$ having the coefficient matrix $A=\begin{bmatrix} 1 & 2 \\ 4 & 3\end{bmatrix}$. Also find the particular solution satisfying the initial condition $\eta=\begin{bmatrix} 3 \\ 3\end{bmatrix}$
Since the fundamental matrix have coloumns $e^{\lambda_it}v_i$, where $\lambda_i$ is the eigenvalues for A and $v_i$ is the eigenvectors of A $(i=1,2)$, i've found the fundamental matrix to be $\Phi(t)=\begin{bmatrix} \frac{1}{2}e^{5t} & -e^{-t} \\ e^{5t} & e^{-t} \end{bmatrix}$
How do I find the particular solution satisfying the initial condition $\eta$?
