ODE No. 1340

\[ y''(x)=\frac {2 (a x+2 b) y'(x)}{x (a x+b)}-\frac {y(x) (2 a x+6 b)}{x^2 (a x+b)} \]

✓ Mathematica : cpu = 0.025259 (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 = 0.033 (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))

\[y \left (x \right ) = \frac {x^{2} \left (c_{2} x +c_{1} \right )}{a x +b}\]