What is a solution to the differential equation #dy/dx=e^(x-y)#?

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Answer 1 · 2016-08-16T07:47:44

# y = ln( e^x + C)#

#dy/dx=e^(x-y) #
#= e^x *e^-y# we can separate it!

#e^y dy/dx= e^x#

#int e^y dy/dx \ dx=int e^x \ dx#

#int e^y \ dy=int e^x \ dx#

# e^y = e^x + C#

#ln ( e^y) =ln( e^x + C)#

# y = ln( e^x + C)#