\[ a y'(x)+y(x) \left (-\left (b^2 x^2+c\right )\right )+y''(x)=0 \] ✓ Mathematica : cpu = 0.023853 (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 = 0.426 (sec), leaf count = 64
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {x \left ( bx+a \right ) }{2}}}}x \left ( {{\sl U}\left ({\frac {{a}^{2}+12\,b+4\,c}{16\,b}},\,{\frac {3}{2}},\,b{x}^{2}\right )}{\it \_C2}+{{\sl M}\left ({\frac {{a}^{2}+12\,b+4\,c}{16\,b}},\,{\frac {3}{2}},\,b{x}^{2}\right )}{\it \_C1} \right ) \right \} \]