Question: Consider the boundary value problem u +4u = 0, 0 x , u(0) = 0, u() = 0. (a) Prove, without solving, that

Consider the boundary value problem uʹʹ +4u = 0, 0 ≤ x ≤ π, u(0) = 0, u(π) = 0.
(a) Prove, without solving, that the set of solutions forms a vector space.
(b) Write this space as the span of one or more functions.

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