Answer:
Step-by-step explanation:
Given Data
Suppose That [tex]y_{1}[/tex] is a solution of L[tex]y_{1}[/tex] = F(x)
and [tex]y_{2}[/tex] is a solution of [tex]Ly_{2}[/tex] = g(x)
L is liner operator
∴ [tex]L(y_{1}+y_{2} )[/tex] = L[tex]y_{1}[/tex] +[tex]Ly_{2}[/tex]
L(y) = F(x) + g(x)
[tex]y_{1}+y_{2}[/tex] is the solution to L(y) = F(x) + g(x)
E.g the liner operator be L = [tex]\frac{d}{dx}[/tex]
[tex]\frac{d}{dx}[/tex] [tex]y_{1}[/tex] = f(x)
[tex]\frac{d}{dx}[/tex] [tex]y_{2}[/tex] = g(x)
[tex]\frac{d}{dx}[/tex] [tex](y_{1}+y_{2} )[/tex] = [tex]\frac{d}{dx}[/tex] [tex]y_{1}[/tex] + [tex]\frac{d}{dx}[/tex] [tex]y_{2}[/tex] = f(x) + g(x)
