\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +a{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( {b}^{2}{x}^{2}+c \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.029504 (sec), leaf count = 101 \[ \left \{\left \{y(x)\to c_1 e^{-\frac {a x}{2}-\frac {b x^2}{2}} H_{\frac {-a^2-4 b-4 c}{8 b}}\left (\sqrt {b} x\right )+c_2 e^{-\frac {a x}{2}-\frac {b x^2}{2}} \, _1F_1\left (-\frac {-a^2-4 b-4 c}{16 b};\frac {1}{2};b x^2\right )\right \}\right \} \]
Maple: cpu = 0.078 (sec), leaf count = 73 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl M}\left ({\frac {{a}^{2} +12\,b+4\,c}{16\,b}},\,{\frac {3}{2}},\,b{x}^{2}\right )}x{{\rm e}^{-{ \frac {x \left ( bx+a \right ) }{2}}}}+{\it \_C2}\,{{\sl U}\left ({\frac {{a}^{2}+12\,b+4\,c}{16\,b}},\,{\frac {3}{2}},\,b{x}^{2}\right )}x{ {\rm e}^{-{\frac {x \left ( bx+a \right ) }{2}}}} \right \} \]