Verify that the indicated pair $of$ functions $is$ a solution $of$ the given system $of$ differential equations $on$ the interval $(-,).$

$\frac{d^{2}x}{d{t}^2}=4y+e^t$

$\frac{d^{2}y}{d{t}^2}=4x-e^t$

$x=cos(2t)+sin(2t)+\frac{1}{5}{e}^t$

$y=-cos(2t)-sin(2t)-\frac{1}{5}{e}^t$

When $x=cos(2t)+sin(2t)+\frac{1}{5}{e}^t,$

$\frac{dx}{dt}=$

$\frac{d^{2}x}{d{t}^2}=$

When $y=-cos(2t)-sin(2t)-\frac{1}{5}{e}^t,$

Thus, $in$ terms $oft,$

$\frac{d^{2}x}{d{t}^2}-4y-e^t=,-4(-cos(2t)-sin(2t)-\frac{1}{5}{e}^t)-e^t$

$=$

and

$\frac{d^{2}y}{d{t}^2}-4x+e^t=,-4(cos(2t)+sin(2t)+\frac{1}{5}{e}^t)+e^t$