Answer
$y(x)=C_1e^{-2x}+C_2e^{2x}+C_3\sin 2x+C_4 \cos 2x$
Work Step by Step
Solve the auxiliary equation for the differential equation. $$r^4+16=0$$
Factor and solve for the roots. $$(r-2)(r+2)(r^2+4)^2$$
Roots are: $r_1=-2, r_2=2, r_3=-2i, r_3=2i$
This implies that 4 are two independent solutions to the differential equation.
Therefore, the general equation is equal to $y(x)=C_1e^{-2x}+C_2e^{2x}+C_3\sin 2x+C_4 \cos 2x$
