\[
\boxed{
{\frac {\rm d}{{\rm d}x}}y \left( x \right) -{x}^{a-1} \left( y \left( x \right)  \right) ^{1-b}f \left( {\frac {{x}^{a}}{a}}+{\frac { \left( y \left( x \right)  \right) ^{b}}{b}} \right) =0}
\]