\[ \left (a x^2+6 n\right ) y'(x)-2 a x y(x)-2 (n+1) x y''(x)+x^2 y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 12.2679 (sec), leaf count = 353
\[\left \{\left \{y(x)\to 2^{-n-\frac {3}{2}} \left (\pi c_3 4^n x^4 \sec (\pi n) \Gamma \left (\frac {3}{2}-n\right ) \left (\sqrt {a} x\right )^{-n-\frac {1}{2}} J_{n+\frac {1}{2}}\left (\sqrt {a} x\right ) \, _1\tilde {F}_2\left (\frac {3}{2}-n;\frac {1}{2}-n,\frac {5}{2}-n;-\frac {a x^2}{4}\right )+\frac {J_{n+\frac {1}{2}}\left (\sqrt {a} x\right ) \left (2 \pi c_3 \left (4 n^2-1\right ) \tan (\pi n) \left (\sqrt {a} x\right )^{n+\frac {1}{2}}+a 2^{n+\frac {1}{2}} \Gamma \left (n+\frac {3}{2}\right ) \left (2 a c_1 x^{n+\frac {1}{2}}-\pi \sqrt {a} c_3 x^3 \tan (\pi n) J_{n-\frac {1}{2}}\left (\sqrt {a} x\right )-2 \pi c_3 x^2 \tan (\pi n) J_{n-\frac {3}{2}}\left (\sqrt {a} x\right )\right )\right )+Y_{n+\frac {1}{2}}\left (\sqrt {a} x\right ) \left (2 \pi c_3 \left (4 n^2-1\right ) \left (\sqrt {a} x\right )^{n+\frac {1}{2}}+a 2^{n+\frac {1}{2}} \Gamma \left (n+\frac {3}{2}\right ) \left (2 a c_2 x^{n+\frac {1}{2}}-\pi \sqrt {a} c_3 x^3 J_{n-\frac {1}{2}}\left (\sqrt {a} x\right )-2 \pi c_3 x^2 J_{n-\frac {3}{2}}\left (\sqrt {a} x\right )\right )\right )}{a^2 \Gamma \left (n+\frac {3}{2}\right )}\right )\right \}\right \}\]
✓ Maple : cpu = 0.291 (sec), leaf count = 53
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{n+{\frac {1}{2}}}{{\sl J}_{-n-{\frac {1}{2}}}\left (\sqrt {a}x\right )}+{\it \_C2}\,{x}^{n+{\frac {1}{2}}}{{\sl Y}_{-n-{\frac {1}{2}}}\left (\sqrt {a}x\right )}+{\it \_C3}\, \left ( a{x}^{2}+4\,n-2 \right ) \right \} \]