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