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