# What is the solution of the Differential Equation # x(dy/dx)+3y+2x^2=x^3+4x #?

# y = (5x^6 - 12x^5+30x^4 + C)/(30x^3) #

We have:

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

So rewrite the equations in standard form as:

Then the integrating factor is given by;

Which we can directly integrate to get:

Confirming the given answer.

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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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