3. General and Particular Solutions of a Differential Equation

General and Particular Solution of a Differential Equation

General(or primitive) solution:

The solution which contains arbitrary constants is called the general(or primitive) solution of the differential equation.

The general solution of the differential equation is of the form y = f(x) or y = ax + b and it has a, b as its arbitrary constants.

Example:

The  function y = a cos x + b sin x, where, a, b Î R is a solution

of the differential equation 

Particular solution:

The solution free from arbitrary constants obtained from the general solution by giving particular values to the arbitrary constants is called a particular solution of the differential equation.

Example: y = e^{– 3x} is a particular solution of the differential equation

Example : The number of arbitrary constants in the general solution of a differential equation

of fourth order are:

1. 0
2.  2
3. 3
4. 4

Ans: D

Example: The number of arbitrary constants in the particular solution of a differential equation

of third order are:

1. 3
2. 2
3. 1
4. 0

Ans: D