I am given a nonhomogeneous differential equation:
where $g(x)=3 \sin 2x$.
After working through the problem, I have
(I was to find a general solution for which $g(x)=0$)
$$y_p(x)=-(24/65) \cos 2x-(3/65) \sin 2x. $$
(On this part, I was given $y_p(x)=A \cos 2x+ B \sin 2x$)
Now I'm stuck. How do I verify that $y_c(x)+y_p(x)$ is a solution to the differential equation?