\[
\boxed{
{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left( x \right) -{a}^{2} \left(  \left( {\frac {\rm d}{{\rm d}x}}y \left( x \right)  \right) ^{5}+2\, \left( {\frac {\rm d}{{\rm d}x}}y \left( x \right)  \right) ^{3}+{\frac {\rm d}{{\rm d}x}}y \left( x \right)  \right) =0}
\]