\[
\boxed{
2\, \left( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left( x \right)  \right) y \left( x \right) - \left( {\frac {\rm d}{{\rm d}x}}y \left( x \right)  \right) ^{2}+f \left( x \right)  \left( y \left( x \right)  \right) ^{2}+a=0}
\]