\[ y''(x)=-\frac {c y(x)}{x^2 (a x+b)^2}-\frac {2 y'(x)}{x} \] ✓ Mathematica : cpu = 0.0337502 (sec), leaf count = 115
DSolve[Derivative[2][y][x] == -((c*y[x])/(x^2*(b + a*x)^2)) - (2*Derivative[1][y][x])/x,y[x],x]
\[\left \{\left \{y(x)\to c_1 \exp \left (\frac {\sqrt {c} \left (-\frac {\sqrt {b^2-4 c}}{\sqrt {c}}-\frac {b}{\sqrt {c}}\right ) (\log (x)-\log (a x+b))}{2 b}\right )+c_2 \exp \left (\frac {\sqrt {c} \left (\frac {\sqrt {b^2-4 c}}{\sqrt {c}}-\frac {b}{\sqrt {c}}\right ) (\log (x)-\log (a x+b))}{2 b}\right )\right \}\right \}\] ✓ Maple : cpu = 0.095 (sec), leaf count = 79
dsolve(diff(diff(y(x),x),x) = -2/x*diff(y(x),x)-c/x^2/(a*x+b)^2*y(x),y(x))
\[y \left (x \right ) = \sqrt {\frac {a x +b}{x}}\, \left (\left (\frac {x}{a x +b}\right )^{-\frac {\sqrt {\frac {b^{2}-4 c}{a^{2}}}\, a}{2 b}} c_{2}+\left (\frac {x}{a x +b}\right )^{\frac {\sqrt {\frac {b^{2}-4 c}{a^{2}}}\, a}{2 b}} c_{1}\right )\]