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**Question:**Show the set of all differentiable functions on (-infinity, +infinity) that satisfy f′ + 2f = 0 is a vector space.

I started the problem by assuming that

**f**and

**g**are both differentiable functions that satisfy this vector space.

Then I ran through the ten axioms of addition and scalar multiplication and proving that each one works.

I feel like that does not answer the question though since why would I need the equation f' + 2f = 0?

How does that equation come into play?

Thanks for any help provided.