Home
Class 12
MATHS
For each of the differential equations ...

For each of the differential equations given below, indicate its order and degree (if defined).(i) `(d^2y)/(dx^2)+5x((dy)/(dx))^2-6x y=logx` (ii) `((dy)/(dx))^3-4((dy)/(dx))^2+7y=sinx`(iii) `(d^4y)/(dx^4)-sin((d^3y)/(dx^3))=0`

Text Solution

Verified by Experts

`(i)` Given differential equation
`(d^(2)y)/(dx^(2))+5x((dy)/(dx))^(2)-6y=logx`
`implies (d^(2)y)/(dx^(2))+5x((dy)/(dx))^(2)-6y-logx=0`
The order with highest derivative in the given differential equation is `2`. Therefore the order of the differential equation is `2` and the degree of highest derivatives is `1`, so the degree of the differential equation is `1`.
`(ii)` Given differential equation
`((dy)/(dx))^(3)-4((dy)/(dx))^(2)+7y=sinx`
`implies((dy)/(dx))^(3)-4((dy)/(dx))^(2)+7y-sinx=0`
Here the derivative with maximum order is `((dy)/(dx))^(3`.
So its order is `1` and degree is `3`.
`(iii)` Given differential equation
`(d^(4)y)/(dx^(4))-sin((d^(3)y)/(dx^(3)))=0`.
The derivative with maximum order is `(d^(4)y)/(dx^(4))`, so the order of the differential equation is `4` but the degree is not defined because `sin((d^(3)y)/(dx^(3)))` is not a polynomial.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN|Exercise Exercise 9.6|19 Videos
  • DETERMINANTS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos
  • INTEGRATION

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|44 Videos

Similar Questions

Explore conceptually related problems

Write the order and degree of x((d^(2)y)/(dx^(2)))+((dy)/(dx))^(3)+y^(2)=0

Find the order and degree (if defined) of the equation: (d^(2)y)/(dx^(2))={1+((dy)/(dx))^(4)}^((5)/(3))

Knowledge Check

  • The degree of the differential equation (d^3y)/(dx^3)+x((dy)/(dx))^4 = 4 log ((d^4y)/(dx^4)) is

    A
    1
    B
    3
    C
    4
    D
    Not defined
  • Similar Questions

    Explore conceptually related problems

    Find the order and degree of (d^3y)/dx^3+2((d^2y)/dx^2)^2-(dy)/(dx)+y=0

    Find order & degree ((dy)/(dx))^(4)+(d^(3)y)/(dx^(3))=3yx(dy)/(dx)

    find order and degree ((d^(2)y)/(dx^(2)))+((dy)/(dx))^(3)+y^(4)=0

    Write order and degree (if defined) of each of the following differential equations. ((dy)/(dx))^(3)-4((dy)/(dx))^(2)+7y=sinx

    find the order and degree of D.E : (1) ((d^(2)y)/(dx^(2) ))^2 + ((dy)/(dx))^(3) = e^(x) (2) sqrt(1 + 1/((dy)/(dx))^(2))= ((d^(2)y)/(dx^(2)))^(3/2) (3) e^((dy)/(dx))+ (dy)/(dx) =x

    Find degree and order x(d^(2)y)/(dx^(2))+((dy)/(dx))^(5)-y(dy)/(dx)=3

    Find the order and degree of the differential equation . (d^(2)y)/(dx)^(2)+x((dy)/(dx))^(3)-1=0