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I need help with converting

$$y' = \sin(x-y)$$

to separable form. What I've done so far is to apply the difference formula:

$$y' = \sin(x)\cos(y) - \cos(x)\sin(y)$$

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up vote 6 down vote accepted

The idea is to get rid of the $\sin$ argument: $ z = x-y$ then $y' = 1-z'$ and you have $$ 1-z' = \sin z \Leftrightarrow z' = 1-\sin z $$ which is an ODE with separated variables and you can easily integrate it.

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