Solve y''+y=[sec(x)sec(x)]

Question

Solve. y'' + y = [sec(x)sec(x)]

Answer 1

Since this has not yet been answered in a while, I will start you off although I cannot give you the whole answer.

The complementary solution is y_c = Ae^ix + Be^-ix which can also be written as

y_c = (A+B) cos x + (A-B)i sin x

I am unable to give you the particular solution to get the sec²x; I am unable to guess at a particular solution to try undetermined coefficients.