\[ \lambda ^2 (-y(x))+x^2 y^{(4)}(x)+6 y''(x)+6 x y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 0.0451337 (sec), leaf count = 156
\[\left \{\left \{y(x)\to c_4 G_{0,4}^{2,0}\left (\frac {\lambda ^2 x^2}{16}|\begin {array}{c} -\frac {1}{2},\frac {1}{2},0,0 \\\end {array}\right )+c_2 G_{0,4}^{2,0}\left (\frac {\lambda ^2 x^2}{16}|\begin {array}{c} 0,0,-\frac {1}{2},\frac {1}{2} \\\end {array}\right )+\frac {c_1 \left (J_1\left (2 \sqrt {\lambda } \sqrt {x}\right )+I_1\left (2 \sqrt {\lambda } \sqrt {x}\right )\right )}{2 \sqrt {\lambda } \sqrt {x}}-\frac {i c_3 \left (I_1\left (2 \sqrt {\lambda } \sqrt {x}\right )-J_1\left (2 \sqrt {\lambda } \sqrt {x}\right )\right )}{4 \sqrt {\lambda } \sqrt {x}}\right \}\right \}\] ✓ Maple : cpu = 0.448 (sec), leaf count = 61
\[ \left \{ y \left ( x \right ) ={ \left ( {\it \_C2}\,{{\sl Y}_{1}\left (2\,\sqrt {\lambda }\sqrt {x}\right )}+{\it \_C1}\,{{\sl J}_{1}\left (2\,\sqrt {\lambda }\sqrt {x}\right )}+{\it \_C3}\,{{\sl J}_{1}\left (2\,\sqrt {-\lambda }\sqrt {x}\right )}+{\it \_C4}\,{{\sl Y}_{1}\left (2\,\sqrt {-\lambda }\sqrt {x}\right )} \right ) {\frac {1}{\sqrt {x}}}} \right \} \]