English

The order and degree of the differential equation dydxdd[1+(dydx)2]2=d2ydx2 respectively, are ______.

Advertisements
Advertisements

Question

The order and degree of the differential equation `[1 + ("dy"/"dx")^2]^2 = ("d"^2y)/("d"x^2)` respectively, are ______.

Options

  • 1, 2

  • 2, 2

  • 2, 1

  • 4, 2

MCQ
Fill in the Blanks
Advertisements

Solution

The order and degree of the differential equation `[1 + ("dy"/"dx")^2]^2 = ("d"^2y)/("d"x^2)` respectively, are 2, 1.

shaalaa.com
  Is there an error in this question or solution?
Chapter 9: Differential Equations - Solved Examples [Page 187]

APPEARS IN

NCERT Exemplar Mathematics Exemplar [English] Class 12
Chapter 9 Differential Equations
Solved Examples | Q 14 | Page 187

RELATED QUESTIONS

Determine the order and degree (if defined) of the differential equation:

`((ds)/(dt))^4 + 3s  (d^2s)/(dt^2) = 0`


Determine the order and degree (if defined) of the differential equation:

y′′′ + 2y″ + y′ = 0


The order of the differential equation `2x^2 (d^2y)/(dx^2) - 3 (dy)/(dx) + y = 0` is ______.


For the differential equation given below, indicate its order and degree (if defined).

`((dy)/(dx))^3 -4(dy/dx)^2 + 7y = sin x`


For the differential equation given below, indicate its order and degree (if defined).

`(d^4y)/dx^4 - sin ((d^3y)/(dx^3)) = 0`


For the given below, verify that the given function (implicit or explicit) is a solution to the corresponding differential equation.

xy = a ex + b e-x + x2 : `x (d^2y)/(dx^2) + 2 dy/dx - xy + x^2 - 2 = 0`


For the given below, verify that the given function (implicit or explicit) is a solution to the corresponding differential equation.

`y = xsin 3x   :   (d^2y)/(dx^2) + 9y - 6 cos 3x = 0`


\[\frac{d^2 y}{d x^2} + 5x\left( \frac{dy}{dx} \right) - 6y = \log x\]

Write the degree of the differential equation \[\left( \frac{dy}{dx} \right)^4 + 3x\frac{d^2 y}{d x^2} = 0\]


The degree of the differential equation \[\frac{d^2 y}{d x^2} + e^\frac{dy}{dx} = 0\]


The degree of the differential equation \[\left\{ 5 + \left( \frac{dy}{dx} \right)^2 \right\}^{5/3} = x^5 \left( \frac{d^2 y}{d x^2} \right)\], is


Determine the order and degree (if defined) of the following differential equation:-

(y"')2 + (y")3 + (y')4 + y5 = 0


Determine the order and degree (if defined) of the following differential equation:-

y" + (y')2 + 2y = 0


In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-

`y=sqrt(1+x^2)`                     `y'=(xy)/(1+x^2)`


Determine the order and degree of the following differential equation:

`root(3)(1 +("dy"/"dx")^2) = ("d"^2"y")/"dx"^2`


Determine the order and degree of the following differential equation:

`("d"^2"y")/"dx"^2 + "dy"/"dx" + "x" = sqrt(1 + ("d"^3"y")/"dx"^3)`


Determine the order and degree of the following differential equation:

`(("d"^2"y")/"dx"^2)^2 + cos ("dy"/"dx") = 0`


Determine the order and degree of the following differential equation:

`("d"^2"y")/"dx"^2 + 5 "dy"/"dx" + "y" = "x"^3`


Determine the order and degree of the following differential equation:

`"dy"/"dx" = 3"y" + root(4)(1 + 5 ("dy"/"dx")^2)`


Determine the order and degree of the following differential equation:

`(("d"^3"y")/"dx"^3)^2 = root(5)(1 + "dy"/"dx")`


Determine the order and degree of the following differential equations.

`(d^4y)/dx^4 + [1+(dy/dx)^2]^3 = 0`


Determine the order and degree of the following differential equations.

`sqrt(1+1/(dy/dx)^2) = (dy/dx)^(3/2)`


Fill in the blank:

Order and degree of a differential equation are always __________ integers.


Order and degree of differential equation are always ______ integers


State whether the following statement is True or False: 

The degree of a differential equation is the power of highest ordered derivative when all the derivatives are made free from negative and/or fractional indices if any


The degree of the differential equation `1/2 ("d"^3"y")/"dx"^3 = {1 + (("d"^2"y")/"dx"^2)}^(5/3)` is ______.


Order of the differential equation representing the family of parabolas y2 = 4ax is ______.


Order of the differential equation representing the family of ellipses having centre at origin and foci on x-axis is two.


The degree of the differential equation `[1 + (("d"y)/("d"x))^2]^(3/2) = ("d"^2y)/("d"x^2)` is ______.


The order and degree of the differential equation `("d"^2y)/("d"x^2) + (("d"y)/("d"x))^(1/4) + x^(1/5)` = 0, respectively, are ______.


The degree of the differential equation `("d"^2y)/("d"x^2) + "e"^((dy)/(dx))` = 0 is ______.


The degree of the differential equation `sqrt(1 + (("d"y)/("d"x))^2)` = x is ______.


The degree and order of the differential equation `[1 + (dy/dx)^3]^(7/3) = 7((d^2y)/(dx^2))` respectively are ______.


The order and degree of the differential equation `sqrt(dy/dx) - 4 dy/dx - 7x` = 0 are ______.


Degree of the differential equation `sinx + cos(dy/dx)` = y2 is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×