The given equation is:

$\frac{dy}{dx} = \frac{\sqrt{x^2 - y^2} + y}{x}$

This is a first-order differential equation involving both $x$ and $y$.

Would you like me to solve this differential equation or analyze it further for a specific method of solution (e.g., separation of variables, substitution, etc.)?

Feel free to ask for additional details!

Here are five questions to expand on the topic:

1. Do you need the general or a specific solution for $y(x)$?
2. Should I check if this equation is separable or exact?
3. Would you like to explore a numerical solution method for this equation?
4. Are you interested in the geometric interpretation of this equation (slope fields)?
5. Should I assist with plotting the solution or any related graph?

Tip: For first-order differential equations, it’s important to first identify whether the equation can be simplified by substitution or if a standard method like integrating factor can be applied.