Let $$L$$ be а secоnd-оrder, lineаr differentiаl equatiоn operator, where$$y_a=e^{4x}$$ is a solution to $$Ly=0$$, and$$y_b=x^2$$ is a solution of the non-homogeneous equation $$Ly = 5x^2$$.Is $$y=3e^{4x}+x^2$$ a solution of $$Ly=5x^2$$? Clearly demonstrate why your answer is correct.