\[ a y(x)-b x^2+x^2 y^{(4)}(x)+2 x y^{(3)}(x)=0 \] ✗ Mathematica : cpu = 300.007 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 0.05 (sec), leaf count = 89
\[ \left \{ y \left ( x \right ) ={\frac {b{x}^{2}}{a}}+{\it \_C1}\,\sqrt {x}{{\sl J}_{1}\left (2\,\sqrt [4]{-a}\sqrt {x}\right )}+{\it \_C2}\,\sqrt {x}{{\sl Y}_{1}\left (2\,\sqrt [4]{-a}\sqrt {x}\right )}+{\it \_C3}\,\sqrt {x}{{\sl J}_{1}\left (2\,\sqrt {-\sqrt {-a}}\sqrt {x}\right )}+{\it \_C4}\,\sqrt {x}{{\sl Y}_{1}\left (2\,\sqrt {-\sqrt {-a}}\sqrt {x}\right )} \right \} \]