Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval $I$ of definition for each solution.
$y'' - 8y' + 20y = 0$; $y = e^{4x} \cos 2x$
When $y = e^{4x} \cos 2x$,
$y' = 4e^{4x} \cos 2x - 2e^{4x} \sin 2x$
$y'' = 4e^{4x} (3 \cos 2x - 4e^{4x} \sin 2x)$
Thus, in terms of $x$,
$y'' - 8y' + 20y = -20e^{4x} \cos 2x + 20e^{4x} \cos 2x$
$= 0$
