- Books Name
- Mathmatics Book Based on NCERT
- Publication
- KRISHNA PUBLICATIONS
- Course
- CBSE Class 12
- Subject
- Mathmatics
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:
- 0
- 2
- 3
- 4
Ans: D
Example: The number of arbitrary constants in the particular solution of a differential equation
of third order are:
- 3
- 2
- 1
- 0
Ans: D