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

Answer 1

Evelyn Agard

# 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)#

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Answer 2

Christopher Agresta

The solution to the differential equation dy/dx = e^(x-y) is given by:

y(x) = ln(cosh(x) + C)

Where C is the constant of integration.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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