हिंदी

The degree of the differential equation dydxdd(1+dydx)3=(d2ydx2)2 is ______.

Advertisements
Advertisements

प्रश्न

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

विकल्प

  • 1

  • 2

  • 3

  • 4

MCQ
रिक्त स्थान भरें
Advertisements

उत्तर

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

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 9: Differential Equations - Solved Examples [पृष्ठ १८७]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
अध्याय 9 Differential Equations
Solved Examples | Q 12 | पृष्ठ १८७

वीडियो ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्न

The degree of the differential equation `((d^2y)/(dx^2))^3 + ((dy)/(dx))^2 + sin ((dy)/(dx)) + 1 = 0` is ______.


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


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

`y = e^x (acos x + b sin x)  :  (d^2y)/(dx^2) - 2 dy/dx + 2y = 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`


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

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

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

Define degree 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 the family of circles touching X-axis at the origin.


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


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


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


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

\[\left( \frac{d^2 y}{{dx}^2} \right)^2 + \left( \frac{dy}{dx} \right)^3 + x^4 = 0 .\]


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 = x sin x              `xy'=y+xsqrt(x^2-y^2)`


Determine the order and degree of the following differential equation:

`"x" + ("d"^2"y")/"dx"^2 = sqrt(1 + (("d"^2"y")/"dx"^2)^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 is True or False:

The order of highest derivative occurring in the differential equation is called degree of the differential equation.


State the degree of differential equation `e^((dy)/(dx)) + (dy)/(dx)` = x


State whether the following statement is True or False:  

The degree of a differential equation `"e"^(-("d"y)/("d"x)) = ("d"y)/("d"x) + "c"` is not defined


Degree of the given differential equation

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


The third order differential equation is ______ 


The differential equation of the family of curves y = ex (A cos x + B sin x). Where A and B are arbitary constants is ______.


The order and degree of the differential equation `("d"^2"y")/"dx"^2 + (("d"^3"y")/"dx"^3) + x^(1/5) = 0` are respectively.


The order of the differential equation of all circles of given radius a is ______.


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


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


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

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


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


Find the general solution of the following differential equation:

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


The order and degree of the differential eqµation whose general solution is given by `(d^2y)/(dx^2) + (dy/dx)^50` = In `((d^2y)/dx^2)` respectively, are ______.


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


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


Find the order and degree of the differential equation `(1 + 3 dy/dx)^(2/3) = 4((d^3y)/(dx^3))`.


Assertion: Degree of the differential equation: `a(dy/dx)^2 + bdx/dy = c`, is 3

Reason: If each term involving derivatives of a differential equation is a polynomial (or can be expressed as polynomial) then highest exponent of the highest order derivative is called the degree of the differential equation.

Which of the following is correct?


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×