\[ 12 x^3 y''(x)-\left (6 x^2+1\right ) y^{(3)}(x)-\left (9 x^2-7\right ) x^2 y'(x)+2 \left (x^2-3\right ) x^3 y(x)+x y^{(4)}(x)=0 \] ✓ Mathematica : cpu = 5.11206 (sec), leaf count = 214
\[\left \{\left \{y(x)\to e^{\frac {x^2}{2}} \left (c_3 \int _1^x \frac {e^{\frac {K[1]^2}{2}} K[1] \left (\int \frac {e^{-\frac {1}{4} \left (1+\sqrt {5}\right ) K[1]^2} \left (K[1]^2\right )^{3/4} U\left (\frac {1}{20} \left (-5-9 \sqrt {5}\right ),-\frac {1}{2},\frac {1}{2} \sqrt {5} K[1]^2\right )}{K[1]^{7/2}} \, dK[1]\right )}{\sqrt [4]{2}} \, dK[1]+c_4 \int _1^x \frac {e^{\frac {K[2]^2}{2}} K[2] \left (\int \frac {e^{-\frac {1}{4} \left (1+\sqrt {5}\right ) K[2]^2} \left (K[2]^2\right )^{3/4} L_{\frac {1}{20} \left (5+9 \sqrt {5}\right )}^{-\frac {3}{2}}\left (\frac {1}{2} \sqrt {5} K[2]^2\right )}{K[2]^{7/2}} \, dK[2]\right )}{\sqrt [4]{2}} \, dK[2]+c_2 e^{\frac {x^2}{2}}+c_1\right )\right \}\right \}\]
✓ Maple : cpu = 0.789 (sec), leaf count = 157
\[ \left \{ y \left ( x \right ) =-{{\rm e}^{{x}^{2}}}\int \!{1{{\sl M}_{{\frac {9\,\sqrt {5}}{20}},\,{\frac {3}{4}}}\left ({\frac {\sqrt {5}{x}^{2}}{2}}\right )}{{\rm e}^{-{\frac {{x}^{2}}{4}}}}{x}^{-{\frac {3}{2}}}}\,{\rm d}x{\it \_C3}-{{\rm e}^{{x}^{2}}}\int \!{1{{\sl W}_{{\frac {9\,\sqrt {5}}{20}},\,{\frac {3}{4}}}\left ({\frac {\sqrt {5}{x}^{2}}{2}}\right )}{{\rm e}^{-{\frac {{x}^{2}}{4}}}}{x}^{-{\frac {3}{2}}}}\,{\rm d}x{\it \_C4}+\int \!{1{{\sl M}_{{\frac {9\,\sqrt {5}}{20}},\,{\frac {3}{4}}}\left ({\frac {\sqrt {5}{x}^{2}}{2}}\right )}{{\rm e}^{{\frac {{x}^{2}}{4}}}}{x}^{-{\frac {3}{2}}}}\,{\rm d}x{{\rm e}^{{\frac {{x}^{2}}{2}}}}{\it \_C3}+{{\rm e}^{{\frac {{x}^{2}}{2}}}}\int \!{1{{\sl W}_{{\frac {9\,\sqrt {5}}{20}},\,{\frac {3}{4}}}\left ({\frac {\sqrt {5}{x}^{2}}{2}}\right )}{{\rm e}^{{\frac {{x}^{2}}{4}}}}{x}^{-{\frac {3}{2}}}}\,{\rm d}x{\it \_C4}+{\it \_C1}\,{{\rm e}^{{x}^{2}}}+{\it \_C2}\,{{\rm e}^{{\frac {{x}^{2}}{2}}}} \right \} \]