\[ y'(x)=\frac {a x^4+a x^3+a x^3 \log (x+1)-x^2 y(x)^2-x y(x)^2+y(x)-x y(x)^2 \log (x+1)}{x} \] ✓ Mathematica : cpu = 0.172582 (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 = 0.25 (sec), leaf count = 48
\[ \left \{ y \left ( x \right ) =\tanh \left ( {\frac {6\,\ln \left ( 1+x \right ) {x}^{2}+4\,{x}^{3}+3\,{x}^{2}-6\,\ln \left ( 1+x \right ) +12\,{\it \_C1}+6\,x+9}{12}\sqrt {a}} \right ) x\sqrt {a} \right \} \]