Answer
$y=c_{1}cos4x+c_{2}sin4x$
Work Step by Step
$y'' + 16y=0$
Auxiliary equation is
$r^{2}+16=0$
$r^{2}=-16$
$r=+\sqrt(-16)$ or $-\sqrt (-16)$
$r= +4\times \sqrt (-1)$ or $-4 \times \sqrt (-1)$
$r= +4i$ or $-4i$
$r_{1}= 0 + i4$
$r_{2}= 0- i4$
$α=0$, $β=4$
$y=e^{αx}(c_{1}cosβx+c_{2}sinβx)$
$y=c_{1}cos4x+c_{2}sin4x$
