Question

5. Consider the differential equation y' + (cost)y = 0 and the vector space C¹ (R) (the vector space of functions having continuous first derivatives on the entire real line). (a) Does the solution set of the differential equation form a subspace of C¹ (R)? If it does, justify your answer. If not, explain why not. (b) If the solution set is a subspace, find a basis and determine the dimension.

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