Can't determine the correct integrating factor (DE)

[darryw]

Homework Statement

Solve (x+2)sin y dx + xcos y dy = 0 by finding integrating factor mu(x)

Homework Equations

i put equation in standard form to get integrating factor

dy/dx + (x+2)sin y / x cos y = 0

but don't i need to get the y out of the sin and cos somehow?

so that y' + p(x)y = q(x)

I could simplify into dy/dx + (x+2/x)tan y = 0 but not sure if that even helps.

I am stuck please help, thanks

The Attempt at a Solution

 

[lippyka]

dy/dx + (x+2)sin y / x cos y = 0 y' + (x+2)sin y / x cos y = 0 p(x)= (x+2)sin y / x cos y q(x) = 0 mu(x) = e^(int p(x) dx)mu(x) = e^ (int (x+2)sin y/xcos y)dx = e^ (int (x+2)/x tan y)dx = e^ (int 1/x tan y)dx + e^ (int 2/x tan y)dx = e^ (ln |x| + int 2/x tan y)dx