The differential equation

y(3)+7y+10y7y=sin(x)\displaystyle {y}^{{{\left({3}\right)}}}+{7}{y}{''}+{10}{y}'-{7}{y}={\sin{{\left({x}\right)}}}

can be rewritten in the form

L(y)=sin(x)\displaystyle {L}{\left({y}\right)}={\sin{{\left({x}\right)}}}

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}=