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**Final Exam / FE-P4**

« **on:**December 14, 2018, 07:55:46 AM »

**Typed solutions only. No uploads**

Find the general solution $(x(t),y(t))$ of the system of ODEs

\begin{equation*}

\left\{\begin{aligned}

&x' = x-2y + \sec(t)\, &&-\frac{\pi}{2}<t<\frac{\pi}{2},\\

&y' = x -\ \,y \,.

\end{aligned}\right.

\end{equation*}

*Hint:*$\sec(t)=\frac{1}{\cos(t)}$.