\[ a y'(x)+y(x) \left (-\left (b^2 x^2+c\right )\right )+y''(x)=0 \] ✓ Mathematica : cpu = 0.0300844 (sec), leaf count = 74
\[\left \{\left \{y(x)\to e^{-\frac {1}{2} x (a+b x)} \left (c_1 H_{-\frac {a^2+4 (b+c)}{8 b}}\left (\sqrt {b} x\right )+c_2 \, _1F_1\left (\frac {a^2+4 (b+c)}{16 b};\frac {1}{2};b x^2\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.102 (sec), leaf count = 64
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {x \left ( bx+a \right ) }{2}}}}x \left ( {{\sl M}\left ({\frac {{a}^{2}+12\,b+4\,c}{16\,b}},\,{\frac {3}{2}},\,b{x}^{2}\right )}{\it \_C1}+{{\sl U}\left ({\frac {{a}^{2}+12\,b+4\,c}{16\,b}},\,{\frac {3}{2}},\,b{x}^{2}\right )}{\it \_C2} \right ) \right \} \]