Chapter 4.9, Problem 14E

In Problems 1–20 solve the given system of differential equations by systematic elimination.

14. $\begin{array}{c}\frac{dx}{dt}+\frac{dy}{dt}=e^t\\ -\frac{d^{2}y}{d{t}^2}+\frac{dx}{dt}+x+y=0\end{array}$