Consider the system of differential equations $$\frac{dx}{dt}=-2 y \qquad\qquad \frac{dy}{dt}=-2 x.$$

Convert this system to a second order differential equation in $y$ by differentiating the second equation with respect to $t$ and substituting for $x$ from the first equation.

Solve the equation you obtained for $y$ as a function of $t$; hence find $x$ as a function of $t$. If we also require $x(0) = 3$ and $y(0) = 1$, what are $x$ and $y$?

$x(t) =$
$y(t) =$