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Answer 1 · 2017-02-18T11:59:57

$y = x-2("arccot"((x+2+C)/(x+C))+k pi)$ , $k = 0,1,2,cdots$

Making $z = x-y$ we have $(dz)/(dx)=1-(dy)/(dx)$ so

$(dy)/(dx)=sin(x-y)-> (dz)/(dx)=1-sin(z)$ This differential equation is separable so

$(dz)/(1-sin(z))=dx$ integrating

$(2sin(z/2))/(cos(z/2)-sin(z/2))=x + C$ or

$2/(cot(z/2)-1)=x+C$ or

$2/(cot((x-y)/2)-1)=x+C$

Finally

$y = x-2("arccot"((x+2+C)/(x+C))+k pi)$