Find the integrating factor for the following differential equation

Question

(cos8x)y′+8(tan8x)y=4sec8x,0<x<π/16.

Answer 1

cos8x y' + 8tan8x y = 4sec8x
as you recall, the IF for
y' + py = q is e^(∫p dx)

Now, if you put your equation into that form, you have

y' + 8(sec8x)(tan8x)y = 4sec^2(8x)

That should look fairly familiar, as far as integrals go.