# What is the general solution of the differential equation # dy/dx- 2xy = x #?

# y = 3/2e^(x^2 - 1) - 1/2 #

We have:

Which we can write as:

Which is a first order separable differential equation, so we can "separate the variables" to get:

Integrating we get, the General Solution:

So we can write an implicit particular solution as:

We typically require an explicit solution, so we can rearrange as follows:

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The general solution of the differential equation ( \frac{dy}{dx} - 2xy = x ) is given by ( y(x) = Ce^{x^2} + \frac{1}{2}x - \frac{1}{4} ), where ( C ) is the constant of integration.

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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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