\[ a^4 y(x)-\lambda (a x-b) \left (y''(x)-a^2 y(x)\right )-2 a^2 y''(x)+y^{(4)}(x)=0 \] ✗ Mathematica : cpu = 300.031 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 0.59 (sec), leaf count = 89
\[ \left \{ y \left ( x \right ) ={{\rm e}^{ax}} \left ( \int \!{{\rm e}^{-2\,ax}} \left ( \int \!{{\rm e}^{ax}} \left ( {{\rm Bi}\left (-{\frac {\lambda \, \left ( ax-b \right ) +{a}^{2}}{a\lambda }\sqrt [3]{-a\lambda }}\right )}{\it \_C4}+{{\rm Ai}\left (-{\frac {\lambda \, \left ( ax-b \right ) +{a}^{2}}{a\lambda }\sqrt [3]{-a\lambda }}\right )}{\it \_C3} \right ) \,{\rm d}x+{\it \_C2} \right ) \,{\rm d}x+{\it \_C1} \right ) \right \} \]