# What is a solution to the differential equation #dy/dx=2e^(x-y)# with the initial condition #y(1)=ln(2e+1)#?

this is separable

So

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The solution to the given differential equation ( \frac{dy}{dx} = 2e^{x-y} ) with the initial condition ( y(1) = \ln(2e+1) ) is:

[ y(x) = -\ln\left(1 + \frac{2e}{e^x}\right) ]

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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.

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.

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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