\[ \text {A0} y(x) (a x+b)+\text {A1} (a x+b) y'(x)+\text {A2} (a x+b)^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.0838542 (sec), leaf count = 243
\[\left \{\left \{y(x)\to c_1 \left (\frac {2 b}{a}+2 x\right )^{\frac {\text {A1}}{2 a \text {A2}}} (2 a \text {A2} x+2 \text {A2} b)^{-\frac {\text {A1}}{2 a \text {A2}}} \left (-\frac {\text {A0} \left (\frac {b}{a}+x\right )}{a \text {A2}}\right )^{\frac {1}{2}-\frac {\text {A1}}{2 a \text {A2}}} I_{\frac {\text {A1}}{a \text {A2}}-1}\left (2 \sqrt {-\frac {\text {A0} \left (\frac {b}{a}+x\right )}{a \text {A2}}}\right )+c_2 (-1)^{1-\frac {\text {A1}}{a \text {A2}}} \left (\frac {2 b}{a}+2 x\right )^{\frac {\text {A1}}{2 a \text {A2}}} (2 a \text {A2} x+2 \text {A2} b)^{-\frac {\text {A1}}{2 a \text {A2}}} \left (-\frac {\text {A0} \left (\frac {b}{a}+x\right )}{a \text {A2}}\right )^{\frac {1}{2}-\frac {\text {A1}}{2 a \text {A2}}} K_{\frac {\text {A1}}{a \text {A2}}-1}\left (2 \sqrt {-\frac {\text {A0} \left (\frac {b}{a}+x\right )}{a \text {A2}}}\right )\right \}\right \}\] ✓ Maple : cpu = 0.08 (sec), leaf count = 98
\[ \left \{ y \left ( x \right ) = \left ( ax+b \right ) ^{-{\frac {-a{\it A2}+{\it A1}}{2\,a{\it A2}}}} \left ( {{\sl Y}_{{\frac {a{\it A2}-{\it A1}}{a{\it A2}}}}\left (2\,\sqrt {{\it A0}}\sqrt {{\frac {ax+b}{{a}^{2}{\it A2}}}}\right )}{\it \_C2}+{{\sl J}_{{\frac {a{\it A2}-{\it A1}}{a{\it A2}}}}\left (2\,\sqrt {{\it A0}}\sqrt {{\frac {ax+b}{{a}^{2}{\it A2}}}}\right )}{\it \_C1} \right ) \right \} \]