- #1

vcb003104

- 19

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## Homework Statement

Show that the set of twice differentiable functions f: R→R satisfying the differential equation

sin(x)f"(x)+[itex]x^{2}[/itex]f(x)=0is a vector space with respect to the usual operations of addition of functions and multiplication by scalars. Here, f" denotes the second derivative of f.

## Homework Equations

sin(x)f"(x)+[itex]x^{2}[/itex]f(x)=0

## The Attempt at a Solution

I have no idea how to start this question.

I know that to prove it is a vector space, proving that it is a subspace is enough?

I flipped through the notes for my course and followed an example done in class. I got :

0(x) = sin(x)0"(x) + [itex]x^{2}[/itex]0(x) = 0