Question

Find a general solution of (4D^2+4D+17)y= 0

Answer 1

The auxiliary equation is

$4m^2+4m+17=0$

$m = \dfrac{-4 \pm \sqrt{16-68}}{8}$

$m = \dfrac{-2 \pm \sqrt{13}i}{4}$

The general solution of the differential equation is

$y = e^{-\frac{1}{2}t}[A\cos( \frac{\sqrt{13}}{4}t) + iB \sin( \frac{\sqrt{13}}{4}t)]$