# What is a solution to the differential equation #(x^2)(e^y)dy/dx=4#?

We can separate the variables:

Integrate both sides:

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To solve the given differential equation ((x^2)(e^y)\frac{dy}{dx}=4), you can rearrange it and integrate both sides with respect to (x). First, divide both sides by (x^2e^y), then integrate with respect to (x).

[\frac{dy}{dx} = \frac{4}{x^2e^y}]

[e^y dy = \frac{4}{x^2} dx]

Now, integrate both sides:

[\int e^y ,dy = \int \frac{4}{x^2} ,dx]

[e^y = -\frac{4}{x} + C]

Where (C) is the constant of integration. This is the general solution to the given differential equation.

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