\[ a^4 y(x)-\lambda (a x-b) \left (y''(x)-a^2 y(x)\right )-2 a^2 y''(x)+y^{(4)}(x)=0 \] ✓ Mathematica : cpu = 48.8374 (sec), leaf count = 141
\[\left \{\left \{y(x)\to c_3 e^{-a x} \int _1^x2 a e^{2 a K[1]} \int e^{-a K[1]} \text {Ai}\left (\frac {a^2+\lambda K[1] a-b \lambda }{(a \lambda )^{2/3}}\right ) \, dK[1]dK[1]+c_4 e^{-a x} \int _1^x2 a e^{2 a K[2]} \int e^{-a K[2]} \text {Bi}\left (\frac {a^2+\lambda K[2] a-b \lambda }{(a \lambda )^{2/3}}\right ) \, dK[2]dK[2]+c_1 e^{-a x}+c_2 e^{a x}\right \}\right \}\] ✓ Maple : cpu = 0.482 (sec), leaf count = 89
\[\left \{y \left (x \right ) = \left (c_{1}+\int \left (c_{2}+\int \left (c_{3} \AiryAi \left (-\frac {\left (-a \lambda \right )^{\frac {1}{3}} \left (a^{2}+\left (a x -b \right ) \lambda \right )}{a \lambda }\right )+c_{4} \AiryBi \left (-\frac {\left (-a \lambda \right )^{\frac {1}{3}} \left (a^{2}+\left (a x -b \right ) \lambda \right )}{a \lambda }\right )\right ) {\mathrm e}^{a x}d x \right ) {\mathrm e}^{-2 a x}d x \right ) {\mathrm e}^{a x}\right \}\]