JEE Exam > JEE Videos > Mathematics (Maths) Class 12 > Differential Equations Representing a Family of Curves
Differential Equations Representing a Family of Curves Video Lecture | Mathematics (Maths) Class 12 - JEE
|
204 videos|290 docs|139 tests
|
FAQs on Differential Equations Representing a Family of Curves Video Lecture - Mathematics (Maths) Class 12 - JEE
| 1. What is a differential equation? |  |
Ans. A differential equation is a mathematical equation that relates a function with its derivatives. It represents the relationship between the rates of change of a function and the function itself.
| 2. How are differential equations used in representing a family of curves? | |
Ans. Differential equations are used to describe the behavior and properties of curves. By solving a differential equation, we can find the equation of a curve that satisfies the given conditions, such as passing through a certain point or having a specific slope at a point.
| 3. Can a differential equation have multiple solutions? | |
Ans. Yes, a differential equation can have multiple solutions. This is because the derivatives of a function can have different values at a given point, resulting in different possible curves that satisfy the equation.
| 4. What is a family of curves? | |
Ans. A family of curves refers to a collection of curves that share a common equation or a set of equations. Each curve in the family represents a specific solution to a differential equation, with different parameters or initial conditions.
| 5. How are differential equations applied in real-life situations? | |
Ans. Differential equations are used in various fields to model and analyze real-life situations. They are commonly used in physics, engineering, biology, economics, and many other disciplines to describe and predict the behavior of systems, such as the motion of objects, population growth, electrical circuits, fluid flow, and more.
Text Transcript from Video
[Music]
in this question for my differential
equation no family of all circles having
sender on the x-axis and radius two
units let the center of the circle be
yes here oh that is on the x-axis so
they so the equation of the circle
having sender a 0 and radius 2 units is
given by X minus a the whole square plus
y minus 0 the whole square equal to 2
square or we can write X minus a the
whole square plus y square equal to 4
differentiating we get with respect to X
we get X minus a 2 plus 2 into Y into dy
by DX equal to 0 or we can write dy by
DX equal to minus of X minus a divided
by Y let this be equation 1 and let this
be version 2 using equation 2 in
equation 1 we get
we can write this is equal to X minus a
equal to minus y into dy by DX using
this formula in equation 1 we get Y into
dy by DX minus the whole square plus y
square equal to 4 or we can write Y
square into dy by DX the whole square
plus y square equal to 4 or we can write
dy by DX the whole square plus 1 equal
to 4 by Y square or dy by DX the whole
square equal to 4 by Y square minus 1 or
we can write dy by DX equal to plus or
minus square root of 4 by Y square minus
1 this is the differential equation
representing the family of circles
[Music]
in this question for my differential
equation no family of all circles having
sender on the x-axis and radius two
units let the center of the circle be
yes here oh that is on the x-axis so
they so the equation of the circle
having sender a 0 and radius 2 units is
given by X minus a the whole square plus
y minus 0 the whole square equal to 2
square or we can write X minus a the
whole square plus y square equal to 4
differentiating we get with respect to X
we get X minus a 2 plus 2 into Y into dy
by DX equal to 0 or we can write dy by
DX equal to minus of X minus a divided
by Y let this be equation 1 and let this
be version 2 using equation 2 in
equation 1 we get
we can write this is equal to X minus a
equal to minus y into dy by DX using
this formula in equation 1 we get Y into
dy by DX minus the whole square plus y
square equal to 4 or we can write Y
square into dy by DX the whole square
plus y square equal to 4 or we can write
dy by DX the whole square plus 1 equal
to 4 by Y square or dy by DX the whole
square equal to 4 by Y square minus 1 or
we can write dy by DX equal to plus or
minus square root of 4 by Y square minus
1 this is the differential equation
representing the family of circles
[Music]
Related Exams
About this Video
|
4.82/5 Rating |
|
Dec 22, 2024 Last updated |
Video Description: Differential Equations Representing a Family of Curves for JEE 2024 is part of Mathematics (Maths) Class 12 preparation.
The notes and questions for Differential Equations Representing a Family of Curves have been prepared according to the JEE exam syllabus.
Information about Differential Equations Representing a Family of Curves covers all important topics for JEE 2024 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for Differential Equations Representing a Family of Curves.
Introduction of Differential Equations Representing a Family of Curves in English is available as part of our Mathematics (Maths) Class 12 for JEE & Differential Equations Representing a Family of Curves in
Hindi for Mathematics (Maths) Class 12 course. Download more important topics related with notes, lectures and mock test series for
JEE Exam by signing up for free.
Description
Video Lecture & Questions for Differential Equations Representing a Family of Curves Video Lecture | Mathematics (Maths) Class 12 - JEE - JEE full syllabus preparation | Free video for JEE exam to prepare for Mathematics (Maths) Class 12.
Information about Differential Equations Representing a Family of Curves
Here you can find the meaning of Differential Equations Representing a Family of Curves defined & explained in the simplest way possible.
Besides explaining types of Differential Equations Representing a Family of Curves theory, EduRev gives you an ample number of questions to practice Differential Equations Representing a Family of Curves tests,
examples and also practice JEE tests.
|
204 videos|290 docs|139 tests
|
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
Semester Notes
,Exam
,Viva Questions
,ppt
,mock tests for examination
,video lectures
,Summary
,Extra Questions
,study material
,Objective type Questions
,Differential Equations Representing a Family of Curves Video Lecture | Mathematics (Maths) Class 12 - JEE
,MCQs
,Previous Year Questions with Solutions
,Differential Equations Representing a Family of Curves Video Lecture | Mathematics (Maths) Class 12 - JEE
,past year papers
,shortcuts and tricks
,Important questions
,practice quizzes
,Differential Equations Representing a Family of Curves Video Lecture | Mathematics (Maths) Class 12 - JEE
,Sample Paper
,Free
;
Study Differential Equations Representing a Family of Curves on the App
Students of JEE can study Differential Equations Representing a Family of Curves alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Differential Equations Representing a Family of Curves,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Differential Equations Representing a Family of Curves is prepared as per the latest JEE syllabus.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup