Could you remind what P_{2}(-inf,inf) is?
The question seems to ask whether the sum of two solutions of 4p''-6p'+2p=0 is again a solution. Well, differentiation is a linear operator...
(apology on the format; I don't know the beginning format for latex)
Is the set W={p (epsilon) C^{2}(-infinity, infinity) | 4p''-6p'+2p=0} a subspace of P_{2}(-inf,inf) with the normal operations of polynomial addition and scalar multiplication?
Can someone give me some advice on how to start?
I am still not sure what P_{2}(-inf,inf) is.
WolframAlpha says that the solutions to 4p''-6p'+2p=0 are for various . These are not polynomials unless .
What I meant is that as a subset of C^{2}(-infinity, infinity), W is a vector space, i..e., it is closed under addition and scalar multiplication. That's why I said that the sum of two solutions is again a solution.