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?