\[ y'(x)=\frac {a x^4+a x^3+a x^3 \log (x+1)-x^2 y(x)^2-x y(x)^2+y(x)-x y(x)^2 \log (x+1)}{x} \] ✓ Mathematica : cpu = 0.0355605 (sec), leaf count = 51
\[\left \{\left \{y(x)\to \sqrt {a} x \tanh \left (\frac {1}{12} \sqrt {a} \left (12 c_1+4 x^3+3 x^2+6 \left (x^2-1\right ) \log (x+1)+6 x\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.077 (sec), leaf count = 48
\[ \left \{ y \left ( x \right ) =\tanh \left ( {\frac {6\,\ln \left ( 1+x \right ) {x}^{2}+4\,{x}^{3}+3\,{x}^{2}-6\,\ln \left ( 1+x \right ) +12\,{\it \_C1}+6\,x+9}{12}\sqrt {a}} \right ) x\sqrt {a} \right \} \]