\[ (a x+b) y'(x)+y(x) (c x+d)+y''(x)=0 \] ✓ Mathematica : cpu = 0.052494 (sec), leaf count = 132
\[\left \{\left \{y(x)\to e^{\frac {c x}{a}-\frac {a x^2}{2}-b x} \left (c_2 \, _1F_1\left (\frac {a^3-d a^2+b c a-c^2}{2 a^3};\frac {1}{2};\frac {\left (x a^2+b a-2 c\right )^2}{2 a^3}\right )+c_1 H_{\frac {-a^3+d a^2-b c a+c^2}{a^3}}\left (\frac {x a^2+b a-2 c}{\sqrt {2} a^{3/2}}\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.106 (sec), leaf count = 98
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {cx}{a}}}} \left ( {{\sl U}\left ({\frac {{a}^{2}d-abc+{c}^{2}}{2\,{a}^{3}}},\,{\frac {1}{2}},\,-{\frac { \left ( {a}^{2}x+ab-2\,c \right ) ^{2}}{2\,{a}^{3}}}\right )}{\it \_C2}+{{\sl M}\left ({\frac {{a}^{2}d-abc+{c}^{2}}{2\,{a}^{3}}},\,{\frac {1}{2}},\,-{\frac { \left ( {a}^{2}x+ab-2\,c \right ) ^{2}}{2\,{a}^{3}}}\right )}{\it \_C1} \right ) \right \} \]