How will you solve:#(dy)/(dx)=e^(x-y)[e^x-e^y]#?

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Answer 1 · 2018-03-21T17:15:52

#y = ln( C_0 e^(-e^x)+e^x-1)#

Making the substitution

#y = ln u# we have the transformed differential equation

#(u'-e^(2x)+e^x u)/u = 0# or assuming #u ne 0#

#u'+e^x u -e^(2x) = 0#

This is a linear non homogeneous differential equation easily soluble giving

#u = C_0 e^(-e^x)+e^x-1# and finally

#y = ln( C_0 e^(-e^x)+e^x-1)#