\[ y''(x)=\frac {2 (a x+2 b) y'(x)}{x (a x+b)}-\frac {y(x) (2 a x+6 b)}{x^2 (a x+b)} \] ✓ Mathematica : cpu = 0.0187352 (sec), leaf count = 32
DSolve[Derivative[2][y][x] == -(((6*b + 2*a*x)*y[x])/(x^2*(b + a*x))) + (2*(2*b + a*x)*Derivative[1][y][x])/(x*(b + a*x)),y[x],x]
\[\left \{\left \{y(x)\to \frac {c_2 x^3}{a x+b}+\frac {c_1 x^2}{a x+b}\right \}\right \}\] ✓ Maple : cpu = 0.021 (sec), leaf count = 20
dsolve(diff(diff(y(x),x),x) = 2/x*(a*x+2*b)/(a*x+b)*diff(y(x),x)-(2*a*x+6*b)/(a*x+b)/x^2*y(x),y(x))
\[y \left (x \right ) = \frac {x^{2} \left (x c_{2}+c_{1}\right )}{a x +b}\]