\[ y'(x)=\frac {\alpha ^3 y(x)^3+\alpha ^3 y(x)^2+\alpha ^3+3 \alpha ^2 \beta x y(x)^2+2 \alpha ^2 \beta x y(x)+3 \alpha \beta ^2 x^2 y(x)+\alpha \beta ^2 x^2+\beta ^3 x^3}{\alpha ^3} \] ✓ Mathematica : cpu = 0.359029 (sec), leaf count = 145
\[\text {Solve}\left [-\frac {1}{3} (29 \alpha +27 \beta )^{2/3} \text {RootSum}\left [\text {$\#$1}^3 (29 \alpha +27 \beta )^{2/3}-3 \text {$\#$1} \alpha ^{2/3}+(29 \alpha +27 \beta )^{2/3}\& ,\frac {\log \left (\frac {\frac {\alpha +3 \beta x}{\alpha }+3 y(x)}{\sqrt [3]{\frac {29 \alpha +27 \beta }{\alpha }}}-\text {$\#$1}\right )}{\alpha ^{2/3}-\text {$\#$1}^2 (29 \alpha +27 \beta )^{2/3}}\& \right ]=\frac {1}{9} x \left (\frac {29 \alpha +27 \beta }{\alpha }\right )^{2/3}+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.058 (sec), leaf count = 42
\[y \relax (x ) = \frac {\RootOf \left (\left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3} \alpha +\textit {\_a}^{2} \alpha +\alpha +\beta }d \textit {\_a} \right ) \alpha -x +c_{1}\right ) \alpha -\beta x}{\alpha }\]