Lineal diferencial equations?

Question

ok. i did this problem but i dont get the book´s anwer.

equation: cosx dy/dx + (senx)y = 1

book´s answer: y = senx + c cosx

Answer 1

Divide by cosx:

dy/dx + ytanx = secx

Integrating factor: e^∫tanxdx = e^-ln|cosx| = e^ln|cosx|^-1 = secx

General solution: ysecx = ∫sec^2xdx + c = tanx + c

==> y = (sinx/cosx).cosx + c cosx = sinx + c cosx