\[ 12 x^3 y''(x)-\left (6 x^2+1\right ) y^{(3)}(x)-\left (9 x^2-7\right ) x^2 y'(x)+2 \left (x^2-3\right ) x^3 y(x)+x y^{(4)}(x)=0 \] ✓ Mathematica : cpu = 5.40737 (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 = 1.833 (sec), leaf count = 157
\[ \left \{ y \left ( x \right ) =-\int \!{1{{\sl W}_{{\frac {9\,\sqrt {5}}{20}},\,{\frac {3}{4}}}\left ({\frac {\sqrt {5}{x}^{2}}{2}}\right )}{{\rm e}^{-{\frac {{x}^{2}}{4}}}}{x}^{-{\frac {3}{2}}}}\,{\rm d}x{{\rm e}^{{x}^{2}}}{\it \_C4}+\int \!{1{{\sl W}_{{\frac {9\,\sqrt {5}}{20}},\,{\frac {3}{4}}}\left ({\frac {\sqrt {5}{x}^{2}}{2}}\right )}{{\rm e}^{{\frac {{x}^{2}}{4}}}}{x}^{-{\frac {3}{2}}}}\,{\rm d}x{{\rm e}^{{\frac {{x}^{2}}{2}}}}{\it \_C4}-{{\rm e}^{{x}^{2}}}\int \!{1{{\sl M}_{{\frac {9\,\sqrt {5}}{20}},\,{\frac {3}{4}}}\left ({\frac {\sqrt {5}{x}^{2}}{2}}\right )}{{\rm e}^{-{\frac {{x}^{2}}{4}}}}{x}^{-{\frac {3}{2}}}}\,{\rm d}x{\it \_C3}+\int \!{1{{\sl M}_{{\frac {9\,\sqrt {5}}{20}},\,{\frac {3}{4}}}\left ({\frac {\sqrt {5}{x}^{2}}{2}}\right )}{{\rm e}^{{\frac {{x}^{2}}{4}}}}{x}^{-{\frac {3}{2}}}}\,{\rm d}x{{\rm e}^{{\frac {{x}^{2}}{2}}}}{\it \_C3}+{\it \_C1}\,{{\rm e}^{{x}^{2}}}+{\it \_C2}\,{{\rm e}^{{\frac {{x}^{2}}{2}}}} \right \} \]