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Differential Equations Representing a Family of Curves Video Lecture | Mathematics (Maths) for JEE Main & Advanced
FAQs on Differential Equations Representing a Family of Curves Video Lecture - Mathematics (Maths) for JEE Main & Advanced
| 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]
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