\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac { \left ( 2\,ax+b \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{x \left ( ax+b \right ) }}-{\frac { \left ( avx-b \right ) y \left ( x \right ) }{ \left ( ax+b \right ) {x}^{2}}}+Ax=0} \]
Mathematica: cpu = 0 (sec), leaf count = 0 \[ \text {Hanged} \]
Maple: cpu = 0.125 (sec), leaf count = 195 \[ \left \{ y \left ( x \right ) = {\mbox {$_2$F$_1$}({\frac {3}{2}}-{\frac {1}{2}\sqrt {1-4\,v}},-{\frac {1}{2}}-{\frac {1}{2}\sqrt {1-4\,v}};\,1-\sqrt {1-4\,v};\,-{\frac {b}{ax}})} {x}^{-{\frac {1}{2}}+{\frac {1}{2}\sqrt {1-4\,v}}}{\it \_C2}+ {\mbox {$_2$F$_1$}({\frac {3}{2}}+{\frac {1}{2}\sqrt {1-4\,v}},-{\frac {1}{2}}+{\frac {1}{2}\sqrt {1-4\,v}};\,1+\sqrt {1-4\,v};\,-{\frac {b}{ax}})} {x}^{-{\frac {1}{2}}-{\frac {1}{2}\sqrt {1-4\,v}}}{\it \_C1}+{\frac { \left ( ax \left ( ax+b \right ) {v}^{2}+ \left ( 8\,{a}^{2}{x}^{2}+6\,ab x-3\,{b}^{2} \right ) v+12\,{a}^{2}{x}^{2}+8\,abx-12\,{b}^{2} \right ) A x}{{a}^{2} \left ( v+6 \right ) \left ( v+2 \right ) \left ( v+12 \right ) }} \right \} \]