# What is the general solution of the differential equation # dy/dx = (x+y)/x #?

# y = xln|x| + Cx #

We have:

Substituting this result into the initial differential equation [A] we get:

Which has reduced the equation to a trivial First Order separable equation, which we can "separate the variables" to get:

And if we integrate we get:

Restoring the earlier substitution, we get:

Leading to the General Solution:

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The general solution of the given differential equation dy/dx = (x+y)/x is y = cx + x, 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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