y ln(x) dx dy

It seems you're presenting a differential equation involving logarithms. However, the notation is a bit unclear. Based on what I can infer, you might be working with the following:

$\frac{dy}{dx} = \frac{y + 1}{x^2} + y \ln(x)$

Is this the equation you're working with? If so, this is a first-order non-homogeneous differential equation. We can solve it step by step.

Let me know if you want a solution for this equation or clarify if you meant something different.

Would you like further details on how to solve this?

Here are 5 related questions:

1. What is a general method for solving first-order differential equations?
2. How does logarithmic differentiation work?
3. What are the methods for solving non-homogeneous differential equations?
4. How can you verify a solution to a differential equation?
5. How do you solve separable differential equations?

Tip: When dealing with logarithmic terms in calculus, recall that the derivative of $\ln(x)$ is $\frac{1}{x}$.