# What is the general solution of the differential equation # 2(y-4x^2)dx+xdy = 0 #?

# y = 2x^2+c/x^2 #

Which we can re-arrange as follows:

We can use an integrating factor when we have a First Order Linear non-homogeneous Ordinary Differential Equation of the form;

Then the integrating factor is given by;

Which we can now directly integrate to get:

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The general solution of the given differential equation is (y = 4x^2 + \frac{C}{x^2}), where (C) is an arbitrary constant.

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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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