\[ y''(x)=-\frac {c y(x)}{x^2 (a x+b)^2}-\frac {2 y'(x)}{x} \] ✓ Mathematica : cpu = 0.0337502 (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 = 0.095 (sec), leaf count = 79
\[y \relax (x ) = \sqrt {\frac {a x +b}{x}}\, \left (\left (\frac {x}{a x +b}\right )^{-\frac {\sqrt {\frac {b^{2}-4 c}{a^{2}}}\, a}{2 b}} c_{2}+\left (\frac {x}{a x +b}\right )^{\frac {\sqrt {\frac {b^{2}-4 c}{a^{2}}}\, a}{2 b}} c_{1}\right )\]