\[
\boxed{
2\, \left( -{x}^{k}+4\,{x}^{3} \right)  \left( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left( x \right) +y \left( x \right) {\frac {\rm d}{{\rm d}x}}y \left( x \right) - \left( y \left( x \right)  \right) ^{3} \right) - \left( k{x}^{k-1}-12\,{x}^{2} \right)  \left( 3\,{\frac {\rm d}{{\rm d}x}}y \left( x \right) + \left( y \left( x \right)  \right) ^{2} \right) +axy \left( x \right) +b=0}
\]