- #1

accountkiller

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## Homework Statement

Let L

_{y}= y'' + py' + qy. Suppose y

_{1}and y

_{2}are functions such that Ly

_{1}= f(x) and Ly

_{2}= g(x). Show that the sum y = y

_{1}+ y

_{2}satisfies the nonhomogeneous equation Ly = f(x) + g(x).

## Homework Equations

Superposition Principle: L[c

_{1}y

_{1}+ c

_{2}y

_{2}] = c

_{1}L[y

_{1}] + c

_{2}L[y

_{2}]

## The Attempt at a Solution

Even though this problem is in the book problems, I don't even see anything with an L

_{y}in the section paragraphs. All we had from lecture is the above superposition principle. I don't even know how to start - I'd really appreciate any help!