\[ -f(x)+y^{(4)}(x)+4 y(x)=0 \] ✓ Mathematica : cpu = 1.40022 (sec), leaf count = 168
\[\left \{\left \{y(x)\to e^{-x} \left (\cos (x) \left (\int _1^x \frac {1}{8} e^{K[1]} f(K[1]) (\cos (K[1])-\sin (K[1])) \, dK[1]\right )+e^{2 x} \cos (x) \left (\int _1^x -\frac {1}{8} e^{-K[4]} f(K[4]) (\sin (K[4])+\cos (K[4])) \, dK[4]\right )+\sin (x) \left (\int _1^x \frac {1}{8} e^{K[2]} f(K[2]) (\sin (K[2])+\cos (K[2])) \, dK[2]\right )+e^{2 x} \sin (x) \left (\int _1^x \frac {1}{8} e^{-K[3]} f(K[3]) (\cos (K[3])-\sin (K[3])) \, dK[3]\right )+c_2 \sin (x)+c_3 e^{2 x} \sin (x)+c_1 \cos (x)+c_4 e^{2 x} \cos (x)\right )\right \}\right \}\]
✓ Maple : cpu = 0.039 (sec), leaf count = 36
\[ \left \{ y \left ( x \right ) ={\frac {f}{4}}+{\it \_C1}\,{{\rm e}^{x}}\cos \left ( x \right ) +{\it \_C2}\,{{\rm e}^{x}}\sin \left ( x \right ) +{\it \_C3}\,{{\rm e}^{-x}}\cos \left ( x \right ) +{\it \_C4}\,{{\rm e}^{-x}}\sin \left ( x \right ) \right \} \]