\[ \boxed { 4\,{\it d4y} \left ( x \right ) -12\,{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) +11\,{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -3\,{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -4\,\cos \left ( x \right ) =0} \]
Mathematica: cpu = 0.098513 (sec), leaf count = 50 \[ \left \{\left \{y(x)\to 2 c_1 e^{x/2}+\frac {2}{3} c_2 e^{3 x/2}+c_3 e^x+c_4+\frac {18 \sin (x)}{65}-\frac {14 \cos (x)}{65}\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 32 \[ \left \{ y \left ( x \right ) =-{\frac {14\,\cos \left ( x \right ) }{65}} +{\frac {18\,\sin \left ( x \right ) }{65}}+{\it \_C1}\,{{\rm e}^{x}}+2 \,{\it \_C2}\,{{\rm e}^{x/2}}+{\frac {2\,{\it \_C3}}{3}{{\rm e}^{{ \frac {3\,x}{2}}}}}+{\it \_C4} \right \} \]