\[ -f(x)+\left (x^2-3\right ) y''(x)+x y^{(3)}(x)+4 x y'(x)+2 y(x)=0 \] ✓ Mathematica : cpu = 1.18487 (sec), leaf count = 340
\[\left \{\left \{y(x)\to \frac {1}{240} \left (240 e^{-\frac {x^2}{2}} x^5 \left (\int _1^x \frac {f(K[1]) \left (8 \sqrt {2 \pi } K[1]^5 \text {erfi}\left (\frac {K[1]}{\sqrt {2}}\right )-15 K[1]^4 \text {Ei}\left (\frac {K[1]^2}{2}\right )+2 e^{\frac {K[1]^2}{2}} \left (-8 K[1]^4+7 K[1]^2+6\right )\right )}{240 K[1]^4} \, dK[1]\right )+8 \sqrt {2 \pi } e^{-\frac {x^2}{2}} x^5 \text {erfi}\left (\frac {x}{\sqrt {2}}\right ) \left (\int _1^x K[2] (-f(K[2])) \, dK[2]\right )+15 x \left (e^{-\frac {x^2}{2}} x^4 \text {Ei}\left (\frac {x^2}{2}\right )-2 \left (x^2+2\right )\right ) \left (\int _1^x f(K[3]) \, dK[3]\right )-16 x^4 \left (\int _1^x K[2] (-f(K[2])) \, dK[2]\right )-16 x^2 \left (\int _1^x K[2] (-f(K[2])) \, dK[2]\right )-48 \int _1^x K[2] (-f(K[2])) \, dK[2]+8 \sqrt {2 \pi } c_2 e^{-\frac {x^2}{2}} x^5 \text {erfi}\left (\frac {x}{\sqrt {2}}\right )+15 c_3 e^{-\frac {x^2}{2}} x^5 \text {Ei}\left (\frac {x^2}{2}\right )-16 c_2 x^4-30 c_3 x^3-16 c_2 x^2+240 c_1 e^{-\frac {x^2}{2}} x^5-60 c_3 x-48 c_2\right )\right \}\right \}\]
✓ Maple : cpu = 0.071 (sec), leaf count = 44
\[ \left \{ y \left ( x \right ) = \left ( {\it \_C3}+\int \!{\frac {2\,{\it \_C1}\,x+{\it \_C2}-\int \!\!\!\int \!-f \left ( x \right ) \,{\rm d}x\,{\rm d}x}{{x}^{6}}{{\rm e}^{{\frac {{x}^{2}}{2}}}}}\,{\rm d}x \right ) {{\rm e}^{-{\frac {{x}^{2}}{2}}}}{x}^{5} \right \} \]