\[ \lambda ^2 (-y(x))+x^2 y^{(4)}(x)+6 x y^{(3)}(x)+6 y''(x)=0 \] ✓ Mathematica : cpu = 0.0457962 (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 = 0.131 (sec), leaf count = 61
\[y \relax (x ) = \frac {c_{2} \BesselY \left (1, 2 \sqrt {\lambda }\, \sqrt {x}\right )+c_{1} \BesselJ \left (1, 2 \sqrt {\lambda }\, \sqrt {x}\right )+c_{3} \BesselJ \left (1, 2 \sqrt {-\lambda }\, \sqrt {x}\right )+c_{4} \BesselY \left (1, 2 \sqrt {-\lambda }\, \sqrt {x}\right )}{\sqrt {x}}\]