\[ y'(x)=\frac {a x^4+a x^3+a x^3 \log (x+1)-x^2 y(x)^2-x y(x)^2+y(x)-x y(x)^2 \log (x+1)}{x} \] ✓ Mathematica : cpu = 0.028784 (sec), leaf count = 80
\[\left \{\left \{y(x)\to \sqrt {a} x \tanh \left (\frac {1}{12} \left (12 \sqrt {a} c_1+4 \sqrt {a} x^3+3 \sqrt {a} x^2+6 \sqrt {a} x^2 \log (x+1)+6 \sqrt {a} x-6 \sqrt {a} \log (x+1)\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.046 (sec), leaf count = 64
\[ \left \{ y \left ( x \right ) =\tanh \left ( {\frac {\ln \left ( 1+x \right ) {x}^{2}}{2}\sqrt {a}}+{\frac {{x}^{3}}{3}\sqrt {a}}+{\frac {{x}^{2}}{4}\sqrt {a}}-{\frac {\ln \left ( 1+x \right ) }{2}\sqrt {a}}+{\it \_C1}\,\sqrt {a}+{\frac {x}{2}\sqrt {a}}+{\frac {3}{4}\sqrt {a}} \right ) x\sqrt {a} \right \} \]