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

Alternative Approach

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The homogeneous solution obeys

To solve this, we will use a technique due to Lagrange (https://tutor.hix.ai)

called the constant variation technique.

#y_h(x)(dc(x))/(dx) + c(x) ((dy_h(x))/(dx)-(2 y_h(x))/x) = x# or

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The solution to the differential equation ( \frac{dy}{dx} = \frac{2y + x^2}{x} ) is given by:

[ y = cx^2 + \frac{2}{3}x^3 - 2x ]

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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