\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {y \left ( x \right ) +{x}^{3}a\ln \left ( 1+x \right ) +a{x}^{4}+a{x}^{3}-x \left ( y \left ( x \right ) \right ) ^{2}\ln \left ( 1+x \right ) -{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}-x \left ( y \left ( x \right ) \right ) ^{2}}{x}}=0} \]
Mathematica: cpu = 0.037505 (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 = 0.047 (sec), leaf count = 64 \[ \left \{ y \left ( x \right ) =\tanh \left ( {\frac {\ln \left ( 1+x \right ) {x}^{2}}{2}\sqrt {a}}+{\frac {{x}^{3}}{3}\sqrt {a}}+{\frac {{ x}^{2}}{4}\sqrt {a}}-{\frac {\ln \left ( 1+x \right ) }{2}\sqrt {a}}+{ \it \_C1}\,\sqrt {a}+{\frac {x}{2}\sqrt {a}}+{\frac {3}{4}\sqrt {a}} \right ) x\sqrt {a} \right \} \]