In finding the general solution, we need the complementary function and particular integral. To find the complementary function, we set the second order derivative to 0 and solve then for the particular integral, we make assumption.

If the second order derivative is equal to $\displaystyle e^{-2x}$, we assume $\displaystyle Ae^{-2x}$, if the second order derivative is equal to $\displaystyle \sin 2x$, we assume $\displaystyle A\cos 2x + B\sin 2x$, but if the second order derivative is equal to the conbination, ie $\displaystyle e^{-2x}\sin 2x$, what do we assume?