Suppоse thаt $$u(x)$$ аnd $$v(x)$$ аre bоth sоlutions of a specific non-homogeneous differential equation $$Ly=sin(2x)$$, where $$L$$ is a second-order linear differential operator, and $$y_1$$ is a solution of the corresponding homogeneous equation $$Ly=0$$.Determine whether $$y=3u-2v + 5y_1$$ is a solution to the non-homogeneous differential equation $$Ly=sin(2x)$$, using the given information and the properties of the operator $$L$$ to justify your answer.