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## Homework Statement

dx/dy = cos(y) - xtan(y)

I need to find the general solution of the problem

## Homework Equations

y' + Py = Q

Where P and Q are functions of x

dy/y = - Pdx

ln(y) = -integral(Pdx)+c

y = e^(-int(Pdx)+c)

## The Attempt at a Solution

Now I have no idea what to do to be honest. Nothing I try and do to separate the variables to get it in the form y' + Py = Q works. There is always something left over that complicates things even more. Ive tried many trig substitutions, to no avail. Here is one thing I tried.

dx/x = [(1/x)cosy - tany]dy

dx/x = (1/x)cosy dy - tan y dy

But then I have two dy terms. Is this correct? I really have no idea how to proceed from here.

Ive also tried:

dx/dy = cos(y) - xtan(y)

(dx/dy)cosy = cos^2(y) - xsiny

(dx/dy)2cosy = 1 + cos(2y) - 2xsiny

But now once again I have no idea how to proceed. Any help would be greatly appreciated!