\[ -\left (9 x^2-7\right ) x^2 y'(x)+12 x^3 y''(x)-\left (6 x^2+1\right ) y^{(3)}(x)+2 \left (x^2-3\right ) x^3 y(x)+x y^{(4)}(x)=0 \] ✓ Mathematica : cpu = 2.89309 (sec), leaf count = 270
\[\left \{\left \{y(x)\to c_3 e^{\frac {x^2}{2}} \int _1^x\frac {e^{\frac {K[1]^2}{2}} \left (\int \frac {\exp \left (\frac {1}{4} \sqrt {5} K[1]^2+\frac {1}{2} \left (-\frac {1}{2} K[1]^2-2 \log (K[1])\right )\right ) U\left (-\frac {-9+\sqrt {5}}{4 \sqrt {5}},-\frac {1}{2},-\frac {1}{2} \sqrt {5} K[1]^2\right )}{\sqrt {K[1]} \sqrt [4]{K[1]^2}} \, dK[1]\right ) K[1]}{\sqrt [4]{2}}dK[1]+c_4 e^{\frac {x^2}{2}} \int _1^x\frac {e^{\frac {K[2]^2}{2}} \left (\int \frac {\exp \left (\frac {1}{4} \sqrt {5} K[2]^2+\frac {1}{2} \left (-\frac {1}{2} K[2]^2-2 \log (K[2])\right )\right ) L_{\frac {-9+\sqrt {5}}{4 \sqrt {5}}}^{-\frac {3}{2}}\left (-\frac {1}{2} \sqrt {5} K[2]^2\right )}{\sqrt {K[2]} \sqrt [4]{K[2]^2}} \, dK[2]\right ) K[2]}{\sqrt [4]{2}}dK[2]+c_1 e^{\frac {x^2}{2}}+c_2 e^{x^2}\right \}\right \}\] ✓ Maple : cpu = 5.928 (sec), leaf count = 157
\[ \left \{ y \left ( x \right ) =-\int \!{{{\sl W}_{{\frac {9\,\sqrt {5}}{20}},\,{\frac {3}{4}}}\left ({\frac {\sqrt {5}{x}^{2}}{2}}\right )}{{\rm e}^{-{\frac {{x}^{2}}{4}}}}{x}^{-{\frac {3}{2}}}}\,{\rm d}x{{\rm e}^{{x}^{2}}}{\it \_C4}+\int \!{{{\sl W}_{{\frac {9\,\sqrt {5}}{20}},\,{\frac {3}{4}}}\left ({\frac {\sqrt {5}{x}^{2}}{2}}\right )}{{\rm e}^{{\frac {{x}^{2}}{4}}}}{x}^{-{\frac {3}{2}}}}\,{\rm d}x{{\rm e}^{{\frac {{x}^{2}}{2}}}}{\it \_C4}-{{\rm e}^{{x}^{2}}}\int \!{{{\sl M}_{{\frac {9\,\sqrt {5}}{20}},\,{\frac {3}{4}}}\left ({\frac {\sqrt {5}{x}^{2}}{2}}\right )}{{\rm e}^{-{\frac {{x}^{2}}{4}}}}{x}^{-{\frac {3}{2}}}}\,{\rm d}x{\it \_C3}+\int \!{{{\sl M}_{{\frac {9\,\sqrt {5}}{20}},\,{\frac {3}{4}}}\left ({\frac {\sqrt {5}{x}^{2}}{2}}\right )}{{\rm e}^{{\frac {{x}^{2}}{4}}}}{x}^{-{\frac {3}{2}}}}\,{\rm d}x{{\rm e}^{{\frac {{x}^{2}}{2}}}}{\it \_C3}+{\it \_C1}\,{{\rm e}^{{x}^{2}}}+{\it \_C2}\,{{\rm e}^{{\frac {{x}^{2}}{2}}}} \right \} \]