\[ a^4 y(x)-\lambda (a x-b) \left (y''(x)-a^2 y(x)\right )-2 a^2 y''(x)+y^{(4)}(x)=0 \] ✗ Mathematica : cpu = 300.028 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 1.322 (sec), leaf count = 92
\[ \left \{ y \left ( x \right ) ={{\rm e}^{ax}} \left ( \int \!{{\rm e}^{-2\,ax}} \left ( \int \!{\it \_C3}\,{{\rm e}^{ax}}{{\rm Ai}\left (-{\frac {\lambda \, \left ( ax-b \right ) +{a}^{2}}{a\lambda }\sqrt [3]{-a\lambda }}\right )}+{\it \_C4}\,{{\rm e}^{ax}}{{\rm Bi}\left (-{\frac {\lambda \, \left ( ax-b \right ) +{a}^{2}}{a\lambda }\sqrt [3]{-a\lambda }}\right )}\,{\rm d}x+{\it \_C2} \right ) \,{\rm d}x+{\it \_C1} \right ) \right \} \]