Basic Concepts
Chapter Name : Differential Equations |
Sub Topic Code : 104_12_09_02_04 |
Topic Name : Basic Concepts |
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Sub Topic Name : Procedure To Form A Differential Equation That Will Represent A Given Family Of Curves |
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Introduction
We can convert any equation (whose both L.H.S and R.H.S are differentiable) into its differential form simply by differentiating its both sides w.r.t any variable. The differential equation represents a family of the curve from which it has been obtained.
Pre-Requisites:
Definite Integration, Indefinite Integration, Differentiation, Limit, Continuity, Differentiability
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
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| Differential Equation | In general, an equation-involving derivative (derivatives) of the dependent variable with respect to independent variable (variables) is called a 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. |
| 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. |
Learning aids / Gadgets
| Gadgets | How it can be used |
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Real life uses :
It is used to represent equation of the family of any curve into its differential form.
Practical examples around us
| Examples | Explainations |
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What you learn in Theory:
How to get a differential equation from its general solution? How to convert equation of any curve into its differential form?