Difference between particular integral and particular solution?

In summary, particular integral and particular solution refer to the same concept of finding a solution to a differential equation. However, the term "particular integral" may not be commonly used in textbooks, while "particular solution" is more widely used. Both terms can be used interchangeably, and there is no significant difference between the two.
  • #1
shivaniits
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difference between particular integral and particular solution..??

particular integral and particular solution are used to find the solution of differential equation..but sometimes they are used interchangeably but what's the difference between two..??
please state examples..!
 
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  • #2


shivaniits said:
particular integral and particular solution are used to find the solution of differential equation..but sometimes they are used interchangeably but what's the difference between two..??
I don't think there is any difference. When I was teaching diff. eqns. none used the "particular integral" terminology, but people have used it often enough here at PF that it must be in use in some texts.
shivaniits said:
please state examples..!
 

1. What is the difference between a particular integral and a particular solution?

A particular integral is a type of solution to a differential equation that is obtained by guessing a function that satisfies the equation. It is not the most general solution, but is specific to the given initial or boundary conditions. A particular solution, on the other hand, is the complete solution that satisfies both the differential equation and the initial or boundary conditions.

2. How are particular integrals and particular solutions used in differential equations?

Particular integrals and particular solutions are used to find the complete solution to a differential equation. The particular integral is used to satisfy the differential equation, while the particular solution is used to satisfy the initial or boundary conditions.

3. Can a particular integral also be a particular solution?

Yes, a particular integral can also be a particular solution. This occurs when the initial or boundary conditions are satisfied by the particular integral, making it the complete solution to the differential equation.

4. Are particular integrals and particular solutions unique?

No, particular integrals and particular solutions are not always unique. For some types of differential equations, there may be multiple particular integrals and particular solutions that satisfy the equation and initial or boundary conditions.

5. What is the significance of particular integrals and particular solutions in real-world applications?

Particular integrals and particular solutions are essential in solving practical problems involving differential equations. They allow us to find the specific solutions that satisfy the given conditions, making it possible to model and predict real-world phenomena such as population growth, chemical reactions, and electrical circuits.

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