\[ a^4 y(x)+2 a^2 y''(x)-\cosh (a x)+y^{(4)}(x)=0 \] ✓ Mathematica : cpu = 0.259547 (sec), leaf count = 47
\[\left \{\left \{y(x)\to \frac {4 a^4 \left (\left (c_4 x+c_3\right ) \sin (a x)+\left (c_2 x+c_1\right ) \cos (a x)\right )+\cosh (a x)}{4 a^4}\right \}\right \}\]
✓ Maple : cpu = 0.523 (sec), leaf count = 51
\[ \left \{ y \left ( x \right ) ={\frac {{{\rm e}^{-ax}}+ \left ( 8\,{\it \_C3}\,x+8\,{\it \_C1} \right ) {a}^{4}\cos \left ( ax \right ) + \left ( 8\,{\it \_C4}\,x+8\,{\it \_C2} \right ) {a}^{4}\sin \left ( ax \right ) +{{\rm e}^{ax}}}{8\,{a}^{4}}} \right \} \]