Without solving, match a solution curve of y" + y = f (x) shown in the figure with one of the following functions:

(i) f (x) = 1,                  (ii) f (x) = e^–x,

(iii) f (x) = e^x,               (iv) f (x) = sin 2x,

(v) f (x) = e^x sin x,        (vi) f (x) = sin x.

Briefly discuss your reasoning.