\[ y'(x)=\frac {a^3+3 a^2 x+3 a x^2+a y(x)^2+x^3+y(x)^3+x y(x)^2}{(a+x)^3} \] ✓ Mathematica : cpu = 1.17545 (sec), leaf count = 106
\[\text {Solve}\left [57 \text {RootSum}\left [-19 \text {$\#$1}^3+6 \sqrt [3]{38} \text {$\#$1}-19\& ,\frac {\log \left (\frac {a+3 y(x)+x}{\sqrt [3]{38} \sqrt [3]{\frac {1}{(a+x)^6}} (a+x)^3}-\text {$\#$1}\right )}{2 \sqrt [3]{38}-19 \text {$\#$1}^2}\& \right ]+38^{2/3} \left (\frac {1}{(a+x)^6}\right )^{2/3} (a+x)^4 \log (a+x)+9 c_1=0,y(x)\right ]\]
✓ Maple : cpu = 0.042 (sec), leaf count = 37
\[ \left \{ y \left ( x \right ) =-{\it RootOf} \left ( -\int ^{{\it \_Z}}\! \left ( {{\it \_a}}^{3}-{{\it \_a}}^{2}-{\it \_a}-1 \right ) ^{-1}{d{\it \_a}}+\ln \left ( x+a \right ) +{\it \_C1} \right ) \left ( x+a \right ) \right \} \]