By choosing a suitable basis, solve the equation

$$\left(\begin{array}{ll} 1 & 2 \\ 1 & 0 \end{array}\right)\left(\begin{array}{l} \dot{x} \\ \dot{y} \end{array}\right)+\left(\begin{array}{cc} -2 & 5 \\ 2 & -1 \end{array}\right)\left(\begin{array}{l} x \\ y \end{array}\right)=e^{-4 t}\left(\begin{array}{c} 3 b \\ 2 \end{array}\right)+e^{-t}\left(\begin{array}{c} -3 \\ c-1 \end{array}\right)$$

subject to the initial conditions $x(0)=0, y(0)=0$.

Explain briefly what happens in the cases $b=2$ or $c=2$.