\[ a y'(x)+y(x) \left (-\left (b^2 x^2+c\right )\right )+y''(x)=0 \] ✓ Mathematica : cpu = 0.0295953 (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 = 0.099 (sec), leaf count = 73
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl M}\left ({\frac {{a}^{2}+12\,b+4\,c}{16\,b}},\,{\frac {3}{2}},\,b{x}^{2}\right )}x{{\rm e}^{-{\frac {x \left ( bx+a \right ) }{2}}}}+{\it \_C2}\,{{\sl U}\left ({\frac {{a}^{2}+12\,b+4\,c}{16\,b}},\,{\frac {3}{2}},\,b{x}^{2}\right )}x{{\rm e}^{-{\frac {x \left ( bx+a \right ) }{2}}}} \right \} \]