https://file.aiquickdraw.com/mathbot/file/172511611080748y1t0tb.jpg

To find the order and degree of a differential equation, we first need to clearly identify the equation. From the uploaded image, the differential equation appears to be:

\[
\frac{d^2y}{dx^2} - \sqrt{\frac{dy}{dx}} = 0
\]

### **Order:**
The order of a differential equation is determined by the highest order derivative present in the equation. In this equation, we have:

- \(\frac{d^2y}{dx^2}\) (second derivative)
- \(\frac{dy}{dx}\) (first derivative)

The highest order derivative is \(\frac{d^2y}{dx^2}\), which is a second-order derivative. Therefore, the order of the differential equation is **2**.

### **Degree:**
The degree of a differential equation is determined by the power of the highest order derivative, provided the differential equation is a polynomial in derivatives. In this case, the term \(\sqrt{\frac{dy}{dx}}\) involves a square root, which makes it non-polynomial in the derivative \(\frac{dy}{dx}\). Thus, the degree of this differential equation is **not defined** because it is not polynomial in its derivatives.

### **Summary:**
- **Order:** 2
- **Degree:** Not defined (because the equation is not polynomial in its derivatives)

Would you like more details, or do you have any questions? Here are some related questions you might consider:

1. What are some examples of differential equations with defined degrees?
2. How do you convert a non-polynomial differential equation into a polynomial one?
3. What are the implications of an undefined degree for solving differential equations?
4. How does the method of solving differ for first-order vs. second-order differential equations?
5. Can you explain how to solve a second-order linear differential equation with constant coefficients?

**Tip:** Always check if the differential equation is polynomial in its derivatives to correctly identify its degree.

Learn how to determine the order and degree of a differential equation using examples. Understand the concept of order as the highest order derivative present and the degree as the power of the highest order derivative in polynomial equations. This problem involves differential equations and their characteristics, suitable for advanced college-level mathematics.

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