\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-2\,{\frac {{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{x}}-{\frac {cy \left ( x \right ) }{{x}^{2} \left ( ax+b \right ) ^{2}}}=0} \]
Mathematica: cpu = 0.050506 (sec), leaf count = 115 \[ \left \{\left \{y(x)\to c_1 \exp \left (\frac {\sqrt {c} \left (-\frac {\sqrt {b^2-4 c}}{\sqrt {c}}-\frac {b}{\sqrt {c}}\right ) (\log (x)-\log (a x+b))}{2 b}\right )+c_2 \exp \left (\frac {\sqrt {c} \left (\frac {\sqrt {b^2-4 c}}{\sqrt {c}}-\frac {b}{\sqrt {c}}\right ) (\log (x)-\log (a x+b))}{2 b}\right )\right \}\right \} \]
Maple: cpu = 0.078 (sec), leaf count = 89 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt {{\frac {ax+b}{x}}} \left ( {\frac {x}{ax+b}} \right ) ^{{\frac {a}{2\,b}\sqrt {{\frac {{b} ^{2}-4\,c}{{a}^{2}}}}}}+{\it \_C2}\,\sqrt {{\frac {ax+b}{x}}} \left ( { \frac {x}{ax+b}} \right ) ^{-{\frac {a}{2\,b}\sqrt {{\frac {{b}^{2}-4\, c}{{a}^{2}}}}}} \right \} \]