$(1$ point$)$ Consider the system of differential equations

$\frac{dx}{dt}=-y,\frac{dy}{dt}=-x$

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 $x(0)=4$ and $y(0)=3,$ what are $x$ and $y?$

$x(t)=$

$y(t)=$