\[ -f(x)+y^{(4)}(x)+4 y(x)=0 \] ✓ Mathematica : cpu = 1.32295 (sec), leaf count = 219
\[\left \{\left \{y(x)\to e^{-x} \left (\cos (x) \int _1^x \frac {1}{8} e^{K[1]} f(K[1]) (\cos (K[1])-\sin (K[1])) \left (\sin ^2(K[1])+\cos ^2(K[1])\right ) \, dK[1]+e^{2 x} \cos (x) \int _1^x -\frac {1}{8} e^{-K[4]} f(K[4]) (\sin (K[4])+\cos (K[4])) \left (\sin ^2(K[4])+\cos ^2(K[4])\right ) \, dK[4]+\sin (x) \left (\int _1^x \frac {1}{8} e^{K[2]} f(K[2]) (\sin (K[2])+\cos (K[2])) \left (\sin ^2(K[2])+\cos ^2(K[2])\right ) \, dK[2]\right )+e^{2 x} \sin (x) \left (\int _1^x \frac {1}{8} e^{-K[3]} f(K[3]) (\cos (K[3])-\sin (K[3])) \left (\sin ^2(K[3])+\cos ^2(K[3])\right ) \, dK[3]\right )\right )+c_2 e^{-x} \sin (x)+c_3 e^x \sin (x)+c_1 e^{-x} \cos (x)+c_4 e^x \cos (x)\right \}\right \}\] ✓ Maple : cpu = 0.021 (sec), leaf count = 36
\[ \left \{ y \left ( x \right ) ={\frac {f}{4}}+{\it \_C1}\,{{\rm e}^{x}}\cos \left ( x \right ) +{\it \_C2}\,{{\rm e}^{x}}\sin \left ( x \right ) +{\it \_C3}\,{{\rm e}^{-x}}\cos \left ( x \right ) +{\it \_C4}\,{{\rm e}^{-x}}\sin \left ( x \right ) \right \} \]