Answer
$y(x)=C_1e^{-2x}+C_2e^{-3x}\cos x+C_3e^{-3x}\sin x$
Work Step by Step
Solve the auxiliary equation for the differential equation. $$r^3+8r^2+22r+20=0$$
Factor and solve for the roots. $$(r+2)(r^2+6r+10)=0$$
Roots are: $r_1=-2, r_2=-3-i,r_3=-3+i$
This implies that 3 are two independent solutions to the differential equation.
Therefore, the general equation is equal to $y(x)=C_1e^{-2x}+C_2e^{-3x}\cos x+C_3e^{-3x}\sin x$
