Find the differential equation correspon...

Find the differential equation corresponding to the family of curves `y=c(x-c)^2` where c is an arbitrary constant.

Text Solution

AI Generated Solution

Doubtnut Promotions Banner Desktop Dark

Doubtnut Promotions Banner Mobile Dark

|

Topper's Solved these Questions

Differential Equation of the First Order
A DAS GUPTA|Exercise Exercise|64 Videos
Definite Integration
A DAS GUPTA|Exercise EXERCISE|62 Videos
Differentiation
A DAS GUPTA|Exercise Exercise|98 Videos

Similar Questions

Explore conceptually related problems

Find the differential equation representing the family of curves y=a.e^(2x)+5 , where a is an arbitrary constant.

Find the differential equation representing the family of curves y=ae^(bx+5), where a and b are arbitrary constants.

Knowledge Check

The degree of the differential equation corresponding to the family of curves y=a(x+a)^(2) , where a is an arbitrary constant is

A

1

B

2

C

3

D

none of these

Which one of the following is the differential equation that represents the family of curves y=(1)/(2x^(2)-c) where c is an arbitrary constant ?

A

`(dy)/(dx)=4xy^(2)`

B

`(dy)/(dx)=1/y`

C

`(dy)/(dx)=x^(2)y`

D

`(dy)/(dx)=-4xy^(2)`

Similar Questions

Explore conceptually related problems

Write the differential equation representing the family of curves y=mx, where m is an arbitrary constant.

Form the differential equation representing the family of curves y^2-2ay+x^2=a^2 , where a is an arbitrary constant.

Form the differential equation representing the family of curves y=a sin(x+b) where a,b are arbitrary constants.

Find the differential equation for the family of curves y^2=4a (x+b) where c is an arbitrary constant.

Find the differential equation of the family of curves y=Ae^(2x)+Be^(-2x), where A and B are arbitrary constants.

Find the differential equation of the family of curves (x+a)^2-2y^2=a^2 , where a is an arbitrary constant.

A DAS GUPTA-Differential Equation of the First Order-Exercise

Find the differential equation corresponding to the family of curves y...
05:38
|
Obtain the differential equation of all conic sections ax^2+by^2=1 whe...
04:17
|
Form the differential equation of the family of circles touching th...
03:34
|
Solve x^2dy+y^2dx=xy(xdy-ydx)
03:35
|
Solve the equation: (1+x^2)tan^-1(dy)/(dx)+y=0
03:46
|
Solve sec^(2)x tany dx+sec^(2)y tanx dy=0
02:55
|
Solve dy/dx+xtan(x+y)+1=0
02:33
|
Solve (x^2+y^2+2xy)dy/dx=a^2
05:33
|
Solve x+y=sin^-1(dy/dx)
05:39
|
Solve (dy)/(dx) sqrt(1+x+y) =x+y-1
13:45
|
Solve x\ dy-y\ dx=sqrt(x^2+y^2)dx
05:50
|
Solve y^2dx+x(x+y)dy=0
05:34
|
Solve x/y*dy/dx=(x-2y)/(x-3y)
03:13
|
(1+e^(x//y))dx+e^(x//y)(1-(x)/(y))dy=0
06:23
|
Solve dy/dx=y/x+tanfrac{y}{x}
04:25
|
Solve (4x-6y+3)dy+(2x-3y-1)dx=0
05:26
|
Solve dy/dx=frac{3x-4y+2}{4x-5y+3}
03:31
|
Solve (2x+4y+1}dy=(2y+x-1)dx
04:12
|
Solve x(x^2+1)(dy)/(dx)=y(1-x^2)+x^2lnx
05:20
|
Solve dy/dx=(1+y^2)/(y(x+y^2+1))
03:38
|