\[ \boxed { {\it A2}\, \left ( ax+b \right ) ^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +{\it A1}\, \left ( ax+b \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +{\it A0}\, \left ( ax+b \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.084011 (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 = 0.046 (sec), leaf count = 117 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( ax+b \right ) ^{-{ \frac {-a{\it A2}+{\it A1}}{2\,a{\it A2}}}}{{\sl J}_{{\frac {a{\it A2} -{\it A1}}{a{\it A2}}}}\left (2\,\sqrt {{\it A0}}\sqrt {{\frac {ax+b}{{ a}^{2}{\it A2}}}}\right )}+{\it \_C2}\, \left ( ax+b \right ) ^{-{\frac { -a{\it A2}+{\it A1}}{2\,a{\it A2}}}}{{\sl Y}_{{\frac {a{\it A2}-{\it A1}}{a{\it A2}}}}\left (2\,\sqrt {{\it A0}}\sqrt {{\frac {ax+b}{{a}^{2} {\it A2}}}}\right )} \right \} \]