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.