What is a particular solution to the differential equation dy/dx=e^(x−y) with y(0)=2?

Sonia Rowland 2022-09-29 Answered
What is a particular solution to the differential equation d y d x = e x - y with y(0)=2?
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Answers (1)

tiepidolu
Answered 2022-09-30 Author has 8 answers
this is separable
d y d x = e x - y = e x e - y
e y d y d x = e x
  e y d y d x   d x =   e x   d x
  e y   d y =   e x   d x
e y = e x + C
y ( 0 ) = 2 e 2 = 1 + C C = e 2 - 1
e y = e x + e 2 - 1
y = ln ( e x + e 2 - 1 )
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