What is the number of arbitrary constant in the particular solution of differential equation of third order ?

Options

A. 0
B. 1
C. 2
D. 3

Answer

To determine the number of arbitrary constants in the particular solution of a third-order differential equation, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Differential Equations**: A differential equation relates a function to its derivatives. The order of a differential equation is determined by the highest derivative present in the equation.

2. **Identifying the Order**: In this case, we are dealing with a third-order differential equation. This means that the highest derivative in the equation is the third derivative.

3. **General Solution of a Differential Equation**: The general solution of a differential equation of order \( n \) contains \( n \) arbitrary constants. This is because each integration introduces a constant.

4. **Applying to Third-Order**: For a third-order differential equation, when we integrate three times to find the general solution, we will introduce three arbitrary constants.

5. **Conclusion**: Therefore, the number of arbitrary constants in the particular solution of a third-order differential equation is 3.

### Final Answer:
The number of arbitrary constants in the particular solution of a third-order differential equation is **3**.

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