English

The degree of the differential equation dydxdd(dydx)2+(d2ydx2)2 = 0 is ______.

Advertisements
Advertisements

Question

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

Fill in the Blanks
Advertisements

Solution

The degree of the differential equation `("dy"/"dx")^2 + (("d"^2y)/("d"x^2))^2` = 0 is Two; since the degree of the highest order derivative is two.

shaalaa.com
  Is there an error in this question or solution?
Chapter 9: Differential Equations - Solved Examples [Page 188]

APPEARS IN

NCERT Exemplar Mathematics Exemplar [English] Class 12
Chapter 9 Differential Equations
Solved Examples | Q 22. (ii) | Page 188

RELATED QUESTIONS

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

`(d^4y)/(dx^4) + sin(y^("')) = 0`


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

y' + 5y = 0


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

`(d^2y)/dx^2 + 5x(dy/dx)^2 - 6y = log x`


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`


\[\frac{d^2 y}{d x^2} = \left( \frac{dy}{dx} \right)^{2/3}\]

\[\left( \frac{d^2 y}{d x^2} \right)^2 + \left( \frac{dy}{dx} \right)^2 = x \sin \left( \frac{d^2 y}{d x^2} \right)\]

\[e^\frac{dy}{dx} = x + 1 ; y\left( 0 \right) = 3\]

Define order of a differential equation.


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


Write the order of the differential equation of all non-horizontal lines in a plane.


Write the order of the differential equation whose solution is y = a cos x + b sin x + c e−x.


What is the degree of the following differential equation?

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

Write the degree of the differential equation \[\left( 1 + \frac{dy}{dx} \right)^3 = \left( \frac{d^2 y}{d x^2} \right)^2\]


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


The order of the differential equation satisfying
\[\sqrt{1 - x^4} + \sqrt{1 - y^4} = a\left( x^2 - y^2 \right)\] is


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

y" + (y')2 + 2y = 0


Find the order and the degree of the differential equation `x^2 (d^2y)/(dx^2) = { 1 + (dy/dx)^2}^4`


Determine the order and degree of the following differential equation:

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


Choose the correct option from the given alternatives:

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


Determine the order and degree of the following differential equations.

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


Fill in the blank:

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


State whether the following statement is true or false:

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


Find the order and degree of the following differential equation:

`[ (d^3y)/dx^3 + x]^(3/2) = (d^2y)/dx^2`


Order of highest derivative occurring in the differential equation is called the ______ of the differential equation


The degree of the differential equation `("d"^4"y")/"dx"^4 + sqrt(1 + ("dy"/"dx")^4)` = 0 is


The order and degree of the differential equation `[1 + 1/("dy"/"dx")^2]^(5/3) = 5 ("d"^2y)/"dx"^2` are respectively.


The order of the differential equation of all circles whose radius is 4, is ______.


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


If m and n are the order and degree of the differential equation `((d^3y)/(dx^3))^6+5((d^3y)/(dx^3))^4/((d^4y)/(dx^4))+(d^4y)/(dx^4)=x^3-1,` then ______.


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


The degree of the differential equation `("d"^2y)/("d"x^2) + 3("dy"/"dx")^2 = x^2 log(("d"^2y)/("d"x^2))` is ______.


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


The degree of the differential equation `("d"^2y)/("d"x^2) + (("d"y)/("d"x))^3 + 6y^5` = 0 is ______.


The degree of the differential equation `("d"^2"y")/("dx"^2) + 3("dy"/"dx")^2 = "x"^2 (("d"^2"y")/("dx"^2))^2` is:


y2 = (x + c)3 is the general solution of the differential equation ______.


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 ______.


The sum of the order and the degree of the differential equation `d/dx[(dy/dx)^3]` is ______.


If `(a + bx)e^(y/x)` = x then prove that `x(d^2y)/(dx^2) = (a/(a + bx))^2`.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×