\[ \boxed { x{\it d4y} \left ( x \right ) - \left ( 6\,{x}^{2}+1 \right ) {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) +12\,{x}^{3}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) - \left ( 9\,{x}^{2}-7 \right ) {x}^{2}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +2\, \left ( {x}^{2}-3 \right ) {x}^{3}y \left ( x \right ) =0} \]
Mathematica: cpu = 7.686976 (sec), leaf count = 262 \[ \left \{\left \{y(x)\to c_3 e^{\frac {x^2}{2}} \int _1^x \frac {e^{\frac {K[1]^2}{2}} K[1] \left (\int \frac {U\left (\frac {1}{20} \left (-5-9 \sqrt {5}\right ),-\frac {1}{2},\frac {1}{2} \sqrt {5} K[1]^2\right ) \exp \left (\frac {1}{2} \left (-\frac {1}{2} K[1]^2-2 \log (K[1])\right )-\frac {1}{4} \sqrt {5} K[1]^2\right )}{\sqrt {K[1]} \sqrt [4]{K[1]^2}} \, dK[1]\right )}{\sqrt [4]{2}} \, dK[1]+c_4 e^{\frac {x^2}{2}} \int _1^x \frac {e^{\frac {K[2]^2}{2}} K[2] \left (\int \frac {L_{\frac {1}{20} \left (5+9 \sqrt {5}\right )}^{-\frac {3}{2}}\left (\frac {1}{2} \sqrt {5} K[2]^2\right ) \exp \left (\frac {1}{2} \left (-\frac {1}{2} K[2]^2-2 \log (K[2])\right )-\frac {1}{4} \sqrt {5} K[2]^2\right )}{\sqrt {K[2]} \sqrt [4]{K[2]^2}} \, dK[2]\right )}{\sqrt [4]{2}} \, dK[2]+c_1 e^{\frac {x^2}{2}}+c_2 e^{x^2}\right \}\right \} \]
Maple: cpu = 0.390 (sec), leaf count = 159 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{{x}^{2}}}+{\it \_C2 }\,{{\rm e}^{{\frac {{x}^{2}}{2}}}}+{\it \_C3}\, \left ( -{{\rm e}^{{x} ^{2}}}\int \!{1{{\sl M}_{{\frac {9\,\sqrt {5}}{20}},\,{\frac {3}{4}} }\left ({\frac {\sqrt {5}{x}^{2}}{2}}\right )}{{\rm e}^{-{\frac {{x}^{2} }{4}}}}{x}^{-{\frac {3}{2}}}}\,{\rm d}x+\int \!{1{{\sl M}_{{\frac {9\, \sqrt {5}}{20}},\,{\frac {3}{4}}}\left ({\frac {\sqrt {5}{x}^{2}}{2}} \right )}{{\rm e}^{{\frac {{x}^{2}}{4}}}}{x}^{-{\frac {3}{2}}}} \,{\rm d}x{{\rm e}^{{\frac {{x}^{2}}{2}}}} \right ) +{\it \_C4}\, \left ( -{{\rm e}^{{x}^{2}}}\int \!{1{{\sl W}_{{\frac {9\,\sqrt {5}}{ 20}},\,{\frac {3}{4}}}\left ({\frac {\sqrt {5}{x}^{2}}{2}}\right )}{ {\rm e}^{-{\frac {{x}^{2}}{4}}}}{x}^{-{\frac {3}{2}}}}\,{\rm d}x+\int \!{1{{\sl W}_{{\frac {9\,\sqrt {5}}{20}},\,{\frac {3}{4}}}\left ({ \frac {\sqrt {5}{x}^{2}}{2}}\right )}{{\rm e}^{{\frac {{x}^{2}}{4}}}}{x }^{-{\frac {3}{2}}}}\,{\rm d}x{{\rm e}^{{\frac {{x}^{2}}{2}}}} \right ) \right \} \]