\[ y'(x)=\frac {a^3+3 a^2 x+3 a x^2+a y(x)^2+x^3+y(x)^3+x y(x)^2}{(a+x)^3} \] ✓ Mathematica : cpu = 0.504701 (sec), leaf count = 111
\[\text {Solve}\left [-\frac {19}{3} \text {RootSum}\left [-19 \text {$\#$1}^3+6 \sqrt [3]{38} \text {$\#$1}-19\& ,\frac {\log \left (\frac {\frac {3 y(x)}{(a+x)^3}+\frac {1}{(a+x)^2}}{\sqrt [3]{38} \sqrt [3]{\frac {1}{(a+x)^6}}}-\text {$\#$1}\right )}{2 \sqrt [3]{38}-19 \text {$\#$1}^2}\& \right ]=\frac {1}{9} 38^{2/3} \left (\frac {1}{(a+x)^6}\right )^{2/3} (a+x)^4 \log (a+x)+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.029 (sec), leaf count = 37
\[\left \{y \left (x \right ) = -\left (a +x \right ) \RootOf \left (c_{1}-\left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3}-\textit {\_a}^{2}-\textit {\_a} -1}d \textit {\_a} \right )+\ln \left (a +x \right )\right )\right \}\]