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

This differential equation is separable, thus we only have to move things around and take integrals.

This looks very familiar. In fact, we can integrate both sides now.

By taking the square root of both sides we get

So, the general solutions to our differential equation are

and

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To solve the differential equation (\frac{dy}{dx} = \frac{e^{-x}}{y}), we can separate the variables and integrate both sides.

Rearrange the equation to separate the variables: [y dy = e^{-x} dx]

Integrate both sides: [\int y dy = \int e^{-x} dx]

This gives: [\frac{1}{2}y^2 = -e^{-x} + C]

Here, (C) is the constant of integration. Therefore, the solution to the differential equation is: [y^2 = -2e^{-x} + C']

Where (C') is a constant that encompasses (2C), which can be determined based on initial conditions or additional information provided.

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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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