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.