\[ -f(x)+\left (x^2-3\right ) y''(x)+4 x y'(x)+x y^{(3)}(x)+2 y(x)=0 \] ✓ Mathematica : cpu = 0.374316 (sec), leaf count = 432
\[\left \{\left \{y(x)\to -\frac {1}{240} e^{-\frac {x^2}{2}} \left (-240 x^5 \int _1^x\left (-\frac {1}{240} \left (15 \text {Ei}\left (\frac {K[1]^2}{2}\right )+16 e^{\frac {K[1]^2}{2}}\right ) f(K[1])+\frac {1}{15} \sqrt {\frac {\pi }{2}} \text {erfi}\left (\frac {K[1]}{\sqrt {2}}\right ) K[1] f(K[1])+\frac {7 e^{\frac {K[1]^2}{2}} f(K[1])}{120 K[1]^2}+\frac {e^{\frac {K[1]^2}{2}} f(K[1])}{20 K[1]^4}\right )dK[1]-8 \sqrt {2 \pi } x^5 \text {erfi}\left (\frac {x}{\sqrt {2}}\right ) \int _1^x-f(K[2]) K[2]dK[2]-15 x^5 \text {Ei}\left (\frac {x^2}{2}\right ) \int _1^xf(K[3])dK[3]+16 e^{\frac {x^2}{2}} x^4 \int _1^x-f(K[2]) K[2]dK[2]+30 e^{\frac {x^2}{2}} x^3 \int _1^xf(K[3])dK[3]+16 e^{\frac {x^2}{2}} x^2 \int _1^x-f(K[2]) K[2]dK[2]+60 e^{\frac {x^2}{2}} x \int _1^xf(K[3])dK[3]+48 e^{\frac {x^2}{2}} \int _1^x-f(K[2]) K[2]dK[2]\right )+\frac {1}{30} c_2 e^{-\frac {x^2}{2}} \left (\sqrt {2 \pi } x^5 \text {erfi}\left (\frac {x}{\sqrt {2}}\right )-2 e^{\frac {x^2}{2}} \left (x^4+x^2+3\right )\right )+\frac {1}{16} c_3 e^{-\frac {x^2}{2}} x^5 \left (\text {Ei}\left (\frac {x^2}{2}\right )-\frac {2 e^{\frac {x^2}{2}} \left (x^2+2\right )}{x^4}\right )+c_1 e^{-\frac {x^2}{2}} x^5\right \}\right \}\] ✓ Maple : cpu = 0.151 (sec), leaf count = 44
\[ \left \{ y \left ( x \right ) = \left ( {\it \_C3}+\int \!{\frac {2\,{\it \_C1}\,x+{\it \_C2}-\int \!\!\!\int \!-f \left ( x \right ) \,{\rm d}x\,{\rm d}x}{{x}^{6}}{{\rm e}^{{\frac {{x}^{2}}{2}}}}}\,{\rm d}x \right ) {{\rm e}^{-{\frac {{x}^{2}}{2}}}}{x}^{5} \right \} \]