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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)#