\[ y^{(4)}(x)+2 y^{(3)}(x)-3 y''(x)-4 y'(x)+4 y(x)-32 \sin (2 x)+24 \cos (2 x)=0 \] ✓ Mathematica : cpu = 0.679589 (sec), leaf count = 40
\[\left \{\left \{y(x)\to \sin (2 x)+c_1 e^{-2 x}+c_2 e^{-2 x} x+c_3 e^x+c_4 e^x x\right \}\right \}\] ✓ Maple : cpu = 0.124 (sec), leaf count = 27
\[\{y \left (x \right ) = \left (c_{3} x +c_{1}\right ) {\mathrm e}^{x}+\left (c_{4} x +c_{2}\right ) {\mathrm e}^{-2 x}+\sin \left (2 x \right )\}\]