Solving math problems

Searching around for something that is interesting to write about and for which there even might be an audience, I've decided I am going to do math problems out of my last university math text book, that being the one I used for a Differential Equations course, Advanced Engineering Mathematics, 6th Edition by Erwin Kreyszig.

Section 1.2, Problem 3

Solve

y'=ky.

Rearranging we get:

y'/y=k

Integrating we have:

∫dy/y = ∫kdx

ln y = kx + C

Section 1.2, Problem 4

Solve

y' = sec y

Rearranging we get:

y' cos y = 1

Integrating we have:

sin y = x + C

y = arc sin x + C

Section 1.2, Problem 5

Solve

y' = y cot x

Rearranging we get:

Integrating we have:

ln |y| = ln |sin x| + C

y = C |sin x|