मराठी

Find the Order and the Degree of the Differential Equation X 2 D 2 Y D X 2 = { 1 + ( D Y D X ) 2 } 4

Advertisements
Advertisements

प्रश्न

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

बेरीज
Advertisements

उत्तर

The highest order derivative present in the given differential equations is `(d^2y)/(dx^2),` so its order is 2.
It is a polynomial `(d^2y)/(dx^2) and dy/dx` and the highest power raised to `(d^2y)/(dx^2)` is 1, so its degree is 1.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2018-2019 (March) 65/1/1

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

Write the degree of the differential equation `x^3((d^2y)/(dx^2))^2+x(dy/dx)^4=0`


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

( y′′′) + (y″)3 + (y′)4 + y5 = 0


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

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


(xy2 + x) dx + (y − x2y) dy = 0


\[\sqrt{1 - y^2} dx + \sqrt{1 - x^2} dx = 0\]

\[y = x\frac{dy}{dx} + a\sqrt{1 + \left( \frac{dy}{dx} \right)^2}\]

Write the order of the differential equation of the family of circles touching X-axis at the origin.


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


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"')2 + (y")3 + (y')4 + y5 = 0


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

y"' + 2y" + y' = 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 equations.

`((d^2y)/(dx^2))^2 + ((dy)/(dx))^2 =a^x `


Determine the order and degree of the following differential equations.

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


State whether the following is True or False:

The degree of the differential equation `e^((dy)/(dx)) = dy/dx +c` is not defined.


Find the order and degree of the following differential equation:

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


Select and write the correct alternative from the given option for the question

The order and degree of `(1 + (("d"y)/("d"x))^3)^(2/3) = 8 ("d"^3y)/("d"x^3)` are respectively


State whether the following statement is True or False: 

Order and degree of differential equation are always positive integers.


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


The differential equation `x((d^2y)/dx^2)^3 + ((d^3y)/dx^3)^2y = x^2` is of ______ 


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


Write the sum of the order and the degree of the following differential equation:

`d/(dx) (dy/dx)` = 5


Find the general solution of the following differential equation:

`(dy)/(dx) = e^(x-y) + x^2e^-y`


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


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


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


Find the order and degree of the differential equation

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


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


What is the key difference between order and degree of a differential equation?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×