\[ \lambda ^2 (-y(x))+x^2 y^{(4)}(x)+6 x y^{(3)}(x)+6 y''(x)=0 \] ✓ Mathematica : cpu = 0.032307 (sec), leaf count = 156
DSolve[-(lambda^2*y[x]) + 6*Derivative[2][y][x] + 6*x*Derivative[3][y][x] + x^2*Derivative[4][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_4 G_{0,4}^{2,0}\left (\frac {\lambda ^2 x^2}{16}|\begin {array}{c} -\frac {1}{2},\frac {1}{2},0,0 \\\end {array}\right )+c_2 G_{0,4}^{2,0}\left (\frac {\lambda ^2 x^2}{16}|\begin {array}{c} 0,0,-\frac {1}{2},\frac {1}{2} \\\end {array}\right )+\frac {c_1 \left (\operatorname {BesselJ}\left (1,2 \sqrt {\lambda } \sqrt {x}\right )+\operatorname {BesselI}\left (1,2 \sqrt {\lambda } \sqrt {x}\right )\right )}{2 \sqrt {\lambda } \sqrt {x}}-\frac {i c_3 \left (\operatorname {BesselI}\left (1,2 \sqrt {\lambda } \sqrt {x}\right )-\operatorname {BesselJ}\left (1,2 \sqrt {\lambda } \sqrt {x}\right )\right )}{4 \sqrt {\lambda } \sqrt {x}}\right \}\right \}\] ✓ Maple : cpu = 0.118 (sec), leaf count = 61
dsolve(x^2*diff(diff(diff(diff(y(x),x),x),x),x)+6*x*diff(diff(diff(y(x),x),x),x)+6*diff(diff(y(x),x),x)-lambda^2*y(x)=0,y(x))
\[y \left (x \right ) = \frac {c_{2} \operatorname {BesselY}\left (1, 2 \sqrt {\lambda }\, \sqrt {x}\right )+c_{1} \operatorname {BesselJ}\left (1, 2 \sqrt {\lambda }\, \sqrt {x}\right )+c_{4} \operatorname {BesselY}\left (1, 2 \sqrt {-\lambda }\, \sqrt {x}\right )+c_{3} \operatorname {BesselJ}\left (1, 2 \sqrt {-\lambda }\, \sqrt {x}\right )}{\sqrt {x}}\]