\[ a^4 y(x)-\lambda (a x-b) \left (y''(x)-a^2 y(x)\right )-2 a^2 y''(x)+y^{(4)}(x)=0 \] ✓ Mathematica : cpu = 268.095 (sec), leaf count = 139
\[\left \{\left \{y(x)\to c_3 e^{-a x} \int _1^x 2 a e^{2 a K[1]} \int e^{-a K[1]} \text {Ai}\left (\frac {a^2+\lambda K[1] a-b \lambda }{(a \lambda )^{2/3}}\right ) \, dK[1] \, dK[1]+c_4 e^{-a x} \int _1^x 2 a e^{2 a K[2]} \int e^{-a K[2]} \text {Bi}\left (\frac {a^2+\lambda K[2] a-b \lambda }{(a \lambda )^{2/3}}\right ) \, dK[2] \, dK[2]+c_1 e^{-a x}+c_2 e^{a x}\right \}\right \}\] ✓ Maple : cpu = 0.559 (sec), leaf count = 89
\[ \left \{ y \left ( x \right ) ={{\rm e}^{ax}} \left ( \int \!{{\rm e}^{-2\,ax}} \left ( \int \!{{\rm e}^{ax}} \left ( {\it \_C4}\,{{\rm Bi}\left (-{\frac {\lambda \, \left ( ax-b \right ) +{a}^{2}}{a\lambda }\sqrt [3]{-a\lambda }}\right )}+{\it \_C3}\,{{\rm Ai}\left (-{\frac {\lambda \, \left ( ax-b \right ) +{a}^{2}}{a\lambda }\sqrt [3]{-a\lambda }}\right )} \right ) \,{\rm d}x+{\it \_C2} \right ) \,{\rm d}x+{\it \_C1} \right ) \right \} \]