\[ y'(x)=\frac {a x^4+a x^3+a x^3 \log (x+1)-x^2 y(x)^2-x y(x)^2+y(x)-x y(x)^2 \log (x+1)}{x} \] ✓ Mathematica : cpu = 0.232307 (sec), leaf count = 80
\[\left \{\left \{y(x)\to \sqrt {a} x \tanh \left (\frac {1}{12} \left (4 \sqrt {a} x^3+3 \sqrt {a} x^2+6 \sqrt {a} x^2 \log (x+1)+6 \sqrt {a} x-6 \sqrt {a} \log (x+1)+12 \sqrt {a} c_1\right )\right )\right \}\right \}\] ✓ Maple : cpu = 0.085 (sec), leaf count = 48
\[\left \{y \left (x \right ) = \sqrt {a}\, x \tanh \left (\frac {\left (4 x^{3}+6 x^{2} \ln \left (x +1\right )+3 x^{2}+12 c_{1}+6 x -6 \ln \left (x +1\right )+9\right ) \sqrt {a}}{12}\right )\right \}\]