Question

The number of arbitrary constants in the particular solution of a differential equation of third order are \(\underline{\hspace{2cm}}\)

Hint:

The order of the differential equation determines the number of arbitrary constants in the general solution.

Answer 1

Step 1: Understanding arbitrary constants.
For a differential equation of order \( n \), the number of arbitrary constants in its particular solution is \( n \).

Step 2: Conclusion.
Thus, for a third-order differential equation, the number of arbitrary constants is 3.