How do you solve the separable differential equation #dy/dx = e^(x-y)#?

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Answer 1 · 2018-03-08T04:19:04

#y = ln(e^x + C)# ; #C \equiv# constant

#dy/dx = e^(x-y)#

#dy/dx = e^xe^-y#

#(dy)/(e^-y) = e^xdx#

#e^y dy = e^x dx#

#inte^ydy = \int e^xdx#

#e^y = e^x + C# ; #C \equiv# constant

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

#y = ln(e^x + C)# ; #C \equiv# constant