The number of arbitrary constants in a particular solution of a differential equation of 4^th order is

The correct option is 0.

To understand why this is the correct answer, let us look at the definitions of the types of solutions of a differential equation:

1. General Solution:
The general solution of a differential equation of n^th order contains exactly n arbitrary constants. For a differential equation of 4^th order, the general solution would contain 4 arbitrary constants.

2. Particular Solution:
A particular solution is obtained from the general solution by assigning specific values to the arbitrary constants based on given boundary or initial conditions. Since all arbitrary constants are replaced by specific numerical values to satisfy the given conditions, a particular solution does not contain any arbitrary constants.

Therefore, the number of arbitrary constants in a particular solution of any differential equation, regardless of its order, is always 0.