\[ \boxed { x{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) + \left ( {x}^{2}-3 \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +4\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +2\,y \left ( x \right ) -f \left ( x \right ) =0} \]
Mathematica: cpu = 0.985125 (sec), leaf count = 431 \[ \left \{\left \{y(x)\to -\frac {1}{240} e^{-\frac {x^2}{2}} \left (-240 x^5 \left (\int _1^x \left (\frac {1}{15} \sqrt {\frac {\pi }{2}} K[1] \text {erfi}\left (\frac {K[1]}{\sqrt {2}}\right ) f(K[1])-\frac {1}{240} \left (15 \text {Ei}\left (\frac {K[1]^2}{2}\right )+16 e^{\frac {K[1]^2}{2}}\right ) f(K[1])+\frac {7 e^{\frac {K[1]^2}{2}} f(K[1])}{120 K[1]^2}+\frac {e^{\frac {K[1]^2}{2}} f(K[1])}{20 K[1]^4}\right ) \, dK[1]\right )-8 \sqrt {2 \pi } x^5 \text {erfi}\left (\frac {x}{\sqrt {2}}\right ) \left (\int _1^x K[2] (-f(K[2])) \, dK[2]\right )-15 x^5 \text {Ei}\left (\frac {x^2}{2}\right ) \left (\int _1^x f(K[3]) \, dK[3]\right )+16 e^{\frac {x^2}{2}} x^2 \left (\int _1^x K[2] (-f(K[2])) \, dK[2]\right )+60 e^{\frac {x^2}{2}} x \left (\int _1^x f(K[3]) \, dK[3]\right )+48 e^{\frac {x^2}{2}} \int _1^x K[2] (-f(K[2])) \, dK[2]+16 e^{\frac {x^2}{2}} x^4 \left (\int _1^x K[2] (-f(K[2])) \, dK[2]\right )+30 e^{\frac {x^2}{2}} x^3 \left (\int _1^x f(K[3]) \, dK[3]\right )\right )+\frac {1}{30} c_2 e^{-\frac {x^2}{2}} \left (\sqrt {2 \pi } x^5 \text {erfi}\left (\frac {x}{\sqrt {2}}\right )-2 e^{\frac {x^2}{2}} \left (x^4+x^2+3\right )\right )+c_3 e^{-\frac {x^2}{2}} x^5 \left (\frac {\text {Ei}\left (\frac {x^2}{2}\right )}{16}+e^{\frac {x^2}{2}} \left (-\frac {1}{4 x^4}-\frac {1}{8 x^2}\right )\right )+c_1 e^{-\frac {x^2}{2}} x^5\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 44 \[ \left \{ y \left ( x \right ) = \left ( {\it \_C3}+\int \!{\frac {2\,x{ \it \_C1}+{\it \_C2}-\int \!\!\!\int \!-f \left ( x \right ) \,{\rm d}x \,{\rm d}x}{{x}^{6}}{{\rm e}^{{\frac {{x}^{2}}{2}}}}}\,{\rm d}x \right ) {{\rm e}^{-{\frac {{x}^{2}}{2}}}}{x}^{5} \right \} \]