Consider the system $of$ differential equations

$\frac{dx}{dt}=-5y,\frac{dy}{dt}=-5x$

Convert this system $to$ a second order differential equation $inyby$ differentiating the second equation with respect $tot$

and substituting for $x$ from the first equation.

Solve the equation you obtained for $yas$ a function $oft$; hence find $xas$ a function $oft.Ifwe$ also require $x(0)=5$ and

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

$x(t)=$

$y(t)=$