# What is the general solution of the differential equation? : #(ylny)dx-xdy=0 #

# y = e^(Ax) #

We have:

This is a separable Differential Equation so we can collect terms and write it in separated differential form and integrate:

The RHS integral is trivial, and the LHS initially seems quite daunting, but if we perform, the substitution:

Substituting into [B], we find

Using this result, we can now integrate [B] to get an Implicit General Solution:

Which is the Explicit General Solution

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The general solution of the given differential equation is:

y * ln(y) = 1/2 * (x^2) + C

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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