Chapter 1.1, Problem 42E

In Problems 41 and 42 verify that the indicated pair of functions is a solution of the given system of differential equations on the interval (−∞, ∞).

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

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

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

y = −cos 2t − sin 2t − $\frac{1}{5}$e^t