Answer
$y(x)=C_1e^{x}+C_2xe^{x}+C_3x^2e^x+C_4 \cos 3x+C_5 \sin 3x$
Work Step by Step
Solve the auxiliary equation for the differential equation. $$(r-1)^3(r^2+9)=0$$
Roots are: $r_1=1$, as a multiplicity of $3$ and $r_2=-3i, r_3=3 i$ as a multiplicity of $1$.
This implies that there are five independent solutions to the differential equation.
Therefore, the general equation is equal to $y(x)=C_1e^{x}+C_2xe^{x}+C_3x^2e^x+C_4 \cos 3x+C_5 \sin 3x$
