\[ \boxed { {\it d4y} \left ( x \right ) +2\,{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) -3\,{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -4\,{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +4\,y \left ( x \right ) -32\,\sin \left ( 2\,x \right ) +24\,\cos \left ( 2\,x \right ) =0} \]
Mathematica: cpu = 0.164521 (sec), leaf count = 40 \[ \left \{\left \{y(x)\to c_1 e^{-2 x}+c_2 e^{-2 x} x+c_3 e^x+c_4 e^x x+\sin (2 x)\right \}\right \} \]
Maple: cpu = 0.046 (sec), leaf count = 31 \[ \left \{ y \left ( x \right ) =\sin \left ( 2\,x \right ) +{\it \_C1}\,{ {\rm e}^{x}}+{\it \_C2}\,{{\rm e}^{-2\,x}}+{\it \_C3}\,x{{\rm e}^{x}}+ {\it \_C4}\,{{\rm e}^{-2\,x}}x \right \} \]