Thread: Is the set a subspace?

(apology on the format; I don't know the beginning format for latex)

Is the set W={p (epsilon) C²(-infinity, infinity) | 4p''-6p'+2p=0} a subspace of P₂(-inf,inf) with the normal operations of polynomial addition and scalar multiplication?

Can someone give me some advice on how to start?

Could you remind what P₂(-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...

would W be a subset because P₂ contains all real numbers?

I don't follow where you get the sum of two solutions.

I am still not sure what P₂(-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 C²(-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.