How do I find the complete solution for x'=(2, 3, -1, -2)x+(e^t, t)?

[Success]

Find the general solution of x'=(2, 3, -1, -2)x+(e^t, t). (this is 2x2 matrix, 2 and 3 on the left, -1 and -2 on the right. and e^t on top, t on bottom. I know that the answer for 2x2 matrix is c1*(1, 1)e^t+c2*(1, 3)e^-t but I don't know how to get the other part.)

 

[Mandelbroth]

Find the general solution of x'=(2, 3, -1, -2)x+(e^t, t). (this is 2x2 matrix, 2 and 3 on the left, -1 and -2 on the right. and e^t on top, t on bottom. I know that the answer for 2x2 matrix is c1*(1, 1)e^t+c2*(1, 3)e^-t but I don't know how to get the other part.)

Your question is unclear. Please use LaTeX. The sample command for a matrix might be $\text{\begin{bmatrix} \alpha & \beta \\ \gamma & \delta\end{bmatrix}}$, which gives $\begin{bmatrix} \alpha & \beta \\ \gamma & \delta\end{bmatrix}$.

Also, this probably should be moved to the homework section.