$$\left. \begin{array} { l } { \frac { d x } { d y } + 4 x + 3 y = t } \\ { \frac { d y } { d 4 } + 2 x + 5 y = e ^ { t } } \end{array} \right.$$
$\left\{\begin{matrix}x=\frac{dt+5d_{4}t-3d_{4}e^{t}}{2\left(2d+7d_{4}\right)}\text{, }y=-\frac{d_{4}\left(t-2e^{t}\right)}{2d+7d_{4}}\text{, }&d\neq -\frac{7d_{4}}{2}\text{ and }d_{4}\neq 0\\x=\frac{t-3y}{4}\text{, }y\in \mathrm{C}\text{, }&t-2e^{t}=0\text{ and }d=-\frac{7d_{4}}{2}\text{ and }d_{4}\neq 0\end{matrix}\right.$
$\left\{\begin{matrix}x=\frac{dt+5d_{4}t-3d_{4}e^{t}}{2\left(2d+7d_{4}\right)}\text{, }y=-\frac{d_{4}\left(t-2e^{t}\right)}{2d+7d_{4}}\text{, }&d\neq -\frac{7d_{4}}{2}\text{ and }d_{4}\neq 0\\x=\frac{t-3y}{4}\text{, }y\in \mathrm{R}\text{, }&t-2e^{t}=0\text{ and }d=-\frac{7d_{4}}{2}\text{ and }d_{4}\neq 0\end{matrix}\right.$
