Integrating Factor Method Problem

[bdh2991]

Homework Statement

Find the general solution of the given differential equation cosxy'+(sinx)y=1

The Attempt at a Solution

I divided everything by cosx and got : y'+(tanx)y=secx

then after doing e to the integral of tanx i got : ∫d/dx[secx*y]=∫secx

after integrating and simplifying i got y= ln|secx+tanx|/secx + Ccosx

the answer in the book is y= sinx + Ccosx

the weakest part of my math is simplifying (or algebra) what did i do wrong or what do i need to do?

 

[vela]

When you multiplied by the integrating factor, you forgot to do it to the righthand side of the equation.