Home
Class 12
MATHS
The differential equation of the family ...

The differential equation of the family of curves `y=e^x(Acosx+Bsinx),` where `A` and `B` are arbitrary constants is

Text Solution

AI Generated Solution

Doubtnut Promotions Banner Mobile Dark
|

Similar Questions

Explore conceptually related problems

Find the differential equation of the family of curves y=e^x(Acosx +Bsinx) where A,B are arbitrary constants. Also write its order and degree.

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

Knowledge Check

  • The differential equation of the family of curves y=e^(x)(A cosx +B sin x) , where A and B are arbitrary constants, is

    A
    `(d^(2)y)/(dx^(2)) -2(dy)/(dx) +2y=0`
    B
    `(d^(2)y)/(dx^(2)) +2(dy)/(dx)-2y=0`
    C
    `(d^(2)y)/(dx^(2)) +((dy)/(dx))^(2) +y=0`
    D
    `(d^(2)y)/(dx^(2))-7(dy)/(dx)+2y=0`

  • The differential equation of the family of curves y=e^(2x)(a cos x+b sin x) where, a and b are arbitrary constants, is given by

    A
    `y_(2)-4y_(1)+5y=0`
    B
    `2y_(2)-y_(1)+5y=0`
    C
    `y_(2)+4y_(1)-5y=0`
    D
    `y_(2)-2y_(1)+5y=0`

  • The differential equation of the family of curves y = p cos (ax) + q sin (ax) , where p , q are arbitrary constants , is :

    A
    `(d^(2) y)/(dx^(2)) - a^(2) y = 0`
    B
    `(d^(2) y)/(dx^(2)) - ay = 0`
    C
    `(d^(2) y)/(dx^(2)) + ay = 0`
    D
    `(d^(2) y)/(dx^(2)) + a^(2) y = 0`

    • Similar Questions

    Explore conceptually related problems

    Find the differential equation of the family of curves,x=A cos nt+B sin nt, where A and B are arbitrary constants.

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

    Form the differential equation of the family of curves y=A cos2x+B sin2x, where A and B are constants.

    The order of the differential equation of the family of curves y=(a)/(c ) sin (bx)+3^(dx) where a, b, c, d are arbitrary constants is

    The differential equation of the family of cruves y = p cos (ax) + q sin (ax) , where p,q are arbitrary constants, is

    Home
    Profile