\[
\boxed{
{\frac {\rm d}{{\rm d}x}}y \left( x \right) ={\frac {{\alpha}^{3}+ \left( y \left( x \right)  \right) ^{2}{\alpha}^{3}+2\,y \left( x \right) {\alpha}^{2}\beta\,x+\alpha\,{\beta}^{2}{x}^{2}+ \left( y \left( x \right)  \right) ^{3}{\alpha}^{3}+3\, \left( y \left( x \right)  \right) ^{2}{\alpha}^{2}\beta\,x+3\,y \left( x \right) \alpha\,{\beta}^{2}{x}^{2}+{\beta}^{3}{x}^{3}}{{\alpha}^{3}}}=0}
\]