General And Particular Solutions Of A Differential Equations
Chapter Name : Differential Equations |
Sub Topic Code : 104_12_09_03_01 |
Topic Name : General And Particular Solutions Of A Differential Equations |
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Sub Topic Name : General And Particular Solutions Of A Differential Equations |
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Introduction
Differential equations are solved mainly by indefinite integration so there always lays the integration constant. The solution of differential equation having integration constant is known as general solution, and we obtain particular solution by assigning the constant a particular value satisfying the given conditions.
Pre-Requisites:
Definite Integration, Indefinite Integration, Differentiation, Limit, Continuity, Differentiability
Activity:
Integration in physical world
Real Life Question:
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Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Degree of a Differential Equation | Degree of a differential equation is the highest power (positive integral index) of the highest order derivative involved in the given differential equation. |
| Order of a Differential Equation | Order of a differential equation is defined as the order of the highest order derivative of the dependent variable with respect to the independent variable involved in the given differential equation. |
| Differential Equation | In general, an equation-involving derivative (derivatives) of the dependent variable with respect to independent variable (variables) is called a differential equation. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Integration chart | To know about Integration |
Real life uses :
It is used widely in various formulas like Newton’s Law of cooling to find the temperature gradient.
Places to visit :
Math libary
Practical examples around us
| Examples | Explainations |
|---|---|
| Integration | Its in physical world |
What you learn in Theory:
What is general and particular solution of a differential equation?
What you learn in Practice:
What is general and particular solution of a differential equation?