Prove the superposition principle for nonhomogeneous equations. Suppose that y1 is a solution to Ly1 = f(x) and y2 is a solution to Ly2 = g(x) (same linear operator L). Show that y = y1 + y2 solves Ly = f(x) + g(x). Differential Equation.

Step-by-step explanation:

Given Data

Suppose That is a solution of L = F(x)

and is a solution  of = g(x)

L is liner operator

∴ = L +

L(y) = F(x) + g(x)

is the solution to  L(y) = F(x) + g(x)

E.g the liner operator be L =

 = f(x)

= g(x)

= + = f(x) + g(x)

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b