Answer
$y(x)=C_1\cos 3x+C_2x\cos 3x+C_3x^2 \cos 3x+C_4 \sin 3x+C_5 x \sin 3x+C_6 x^2 \sin 3x$
Work Step by Step
Solve the auxiliary equation for the differential equation. $$(r^2+9)=0$$
Roots are: $r_1=-3i$, as a multiplicity of $3$ and $r_2=3i$ as a multiplicity of $3$.
This implies that there are $\bf{Six}$ independent solutions to the differential equation .
Therefore, the general equation is equal to $y(x)=C_1\cos 3x+C_2x\cos 3x+C_3x^2 \cos 3x+C_4 \sin 3x+C_5 x \sin 3x+C_6 x^2 \sin 3x$
