The differential equation

y(4)+9y(3)y+5y=ex\displaystyle {y}^{{{\left({4}\right)}}}+{9}{y}^{{{\left({3}\right)}}}-{y}{''}+{5}{y}={e}^{{x}}

can be rewritten in the form

L(y)=ex\displaystyle {L}{\left({y}\right)}={e}^{{x}}

where L\displaystyle {L} is a differential operator based on D=ddx\displaystyle {D}=\frac{{d}}{{{\left.{d}{x}\right.}}}. Find L\displaystyle {L}.

L=\displaystyle {L}=