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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.

Solve the differential equation: dy/dx = (sqrt(x^2 - y^2) + y) / x.

Explore a step-by-step approach to solve the first-order differential equation dy/dx = (sqrt(x^2 - y^2) + y) / x. Learn about key calculus concepts, including differential equations, and methods like substitution and separation of variables. Suitable for undergraduate students.

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