Order of highest derivative occurring in the differential equation is called the degree of the differential equation

Answer

To determine whether the statement "The order of the highest derivative occurring in the differential equation is called the degree of the differential equation" is true or false, we need to clarify the definitions of "order" and "degree" in the context of differential equations.

### Step-by-Step Solution:

1. **Understanding Order and Degree:**
- The **order** of a differential equation is defined as the highest derivative present in the equation. For example, in the equation \( \frac{d^3y}{dx^3} + \frac{d^2y}{dx^2} + y = 0 \), the highest derivative is \( \frac{d^3y}{dx^3} \), so the order is 3.
- The **degree** of a differential equation is defined as the power of the highest order derivative when the equation is a polynomial in derivatives.

2. **Identifying the Statement:**
- The statement claims that the order of the highest derivative is called the degree of the differential equation. This is incorrect because the order and degree are two different concepts.

3. **Condition for Degree:**
- For the degree to be defined, the differential equation must be a polynomial in derivatives and must not contain any radical signs or fractional powers of the derivatives. For example, if we have \( \left( \frac{d^2y}{dx^2} \right)^{1/2} \), this introduces a radical, and we cannot define the degree in this case.

4. **Conclusion:**
- Therefore, the statement is false as it conflates the definitions of order and degree. The correct statement would be: "The order of the highest derivative occurring in the differential equation is called the order of the differential equation, while the degree is defined only when the equation is a polynomial in derivatives."

### Final Answer:
The statement is **False**.