Home
Class 12
MATHS
If the differential equation of the fami...

If the differential equation of the family of curve given by `y=Ax+Be^(2x),` where A and B are arbitary constants is of the form
`(1-2x)(d)/(dx)((dy)/(dx)+ly)+k((dy)/(dx)+ly)=0,` then the ordered pair (k,l) is

A

(2,-2)

B

(-2,2)

C

(2,2)

D

(-2,-2)

Text Solution

Verified by Experts

The correct Answer is:
A
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|13 Videos
  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|9 Videos
  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise For Session 5|8 Videos
  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos
  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise For Session 10|4 Videos

Similar Questions

Explore conceptually related problems

[" The differential equation of the family of curves "],[y=c_(1)x^(3)+(c_(2))/(x)" where "c_(1)" and "c_(2)" are arbitrary "],[" constants,is "],[" O "x^(2)(d^(2)y)/(dx^(2))-x(dy)/(dx)-3y=0],[" (x) "(d^(2)y)/(dx^(2))+x(dy)/(dx)+3y=0],[" (x) "(d^(2)y)/(dx^(2))+x(dy)/(dx)-3y=0],[" (x) "(d^(2)y)/(dx^(2))-x(dy)/(dx)+3y=0]

The differential equation of which y=ax^(2)+bx is the general solution, a, b being arbitrary constants is x^(2)(d^(2)y)/(dx^(2))-2x(dy)/(dx) +2y=0 .

Knowledge Check

  • The differential equation of the family of curves y=k_(1)x^(2)+k_(2) is given by (where, k_(1) and k_(2) are arbitrary constants and y_(1)=(dy)/(dx), y_(2)=(d^(2)y)/(dx^(2)) )

    A
    `y_(1)=x^(2)y_(2)`
    B
    `(y_(1))^(2)=xy_(2)`
    C
    `xy_(2)=y_(1)`
    D
    `y_(1)y_(2)=x`
  • The degree of the differential equation ((d^2y)/(dx^2))^2+((dy)/(dx))^2="sin "((dy)/(dx)) is

    A
    1
    B
    2
    C
    3
    D
    not defined
  • The differential equation x(dy)/(dx)+(3)/((dy)/(dx))=y^(2)

    A
    is of order 1
    B
    is of degree 2
    C
    is linear
    D
    is non-linear
  • Similar Questions

    Explore conceptually related problems

    Solve the differential equation x(d^2y)/dx^2=1 , given that y=1, (dy)/(dx)=0 when x=1

    The differential equation of the family of curves whose equation is (x-h)^2+(y-k)^2=a^2 , where a is a constant, is (A) [1+(dy/dx)^2]^3=a^2 (d^2y)/dx^2 (B) [1+(dy/dx)^2]^3=a^2 ((d^2y)/dx^2)^2 (C) [1+(dy/dx)]^3=a^2 ((d^2y)/dx^2)^2 (D) none of these

    Which one of the following differential equations represents the family of straight lines which are at unit distance from the origin a) (y-x(dy)/(dx))^2=1-((dy)/(dx))^2 b) (y+x(dy)/(dx))^2=1+((dy)/(dx))^2 c)(y-x(dy)/(dx))^2=1+((dy)/(dx))^2 d) (y+x(dy)/(dx))^2=1-((dy)/(dx))^2

    solve the differential equation x(d^2y)/dx^2+dy/dx=0 .

    Solve the differential equation x(d^(2)y)/(dx^(2))+(dy)/(dx)+x=0