\[
\boxed{
{\frac {\rm d}{{\rm d}x}}y \left( x \right) ={\frac {{a}^{2}x+{a}^{3}{x}^{3}+{a}^{3}{x}^{3} \left( y \left( x \right)  \right) ^{2}+2\,{a}^{2}{x}^{2}y \left( x \right) +ax+ \left( y \left( x \right)  \right) ^{3}{a}^{3}{x}^{3}+3\, \left( y \left( x \right)  \right) ^{2}{a}^{2}{x}^{2}+3\,axy \left( x \right) +1}{{a}^{3}{x}^{3}}}=0}
\]