Answer
$y(x)=C_1e^{-4x}\cos 2 x+C_2 e^{-4x}\sin 2x$.
Work Step by Step
Solve the characteristic equation for the differential equation. $$r^2+8r+20=0$$
Factor and solve for the roots. $$r_1=-4-2i ; r_2=-4+2i$$ as roots.
This implies that there are two independent solutions to the differential equation $y_1(x)=e^{- 4x}\cos 2x$ and $y_2= e^{-4x}\sin 2x$.
Therefore, the general equation is equal to $y(x)=C_1e^{-4x}\cos 2 x+C_2 e^{-4x}\sin 2x$.
