मराठी

The degree of the differential equation dddydxddd2ydx2+3(dydx)2=x2log(d2ydx2) is ______. - Mathematics

Advertisements
Advertisements

प्रश्न

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

पर्याय

  • 1

  • 2

  • 3

  • not defined

MCQ
रिकाम्या जागा भरा

उत्तर

The degree of the differential equation `("d"^2y)/("d"x^2) + 3("dy"/"dx")^2 = x^2 log(("d"^2y)/("d"x^2))` is not defined.

Explanation:

The given differential equation is not a polynomial equation in terms of its derivatives

So its degree is not defined.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 9: Differential Equations - Solved Examples [पृष्ठ १८७]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
पाठ 9 Differential Equations
Solved Examples | Q 13 | पृष्ठ १८७

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

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

y′ + y = ex


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.

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


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

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

Write the degree of the differential equation
\[a^2 \frac{d^2 y}{d x^2} = \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^{1/4}\]


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

\[\left( \frac{ds}{dt} \right)^4 + 3s\frac{d^2 s}{d t^2} = 0\]


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

y" + 2y' + sin y = 0


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

y = cos x + C            y' + sin x = 0


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"^3"y")/"dx"^3)^(1/2) - ("dy"/"dx")^(1/3) = 20`


Determine the order and degree of the following differential equation:

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


Determine the order and degree of the following differential equations.

`(y''')^2 + 2(y'')^2 + 6y' + 7y = 0`


Determine the order and degree of the following differential equations.

`((d^3y)/dx^3)^(1/6) = 9`


Choose the correct alternative.

The order and degree of `[ 1+ (dy/dx)^3]^(2/3) = 8 (d^3y)/dx^3` are respectively.


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


Order and degree of differential equation`(("d"^3y)/("d"x^3))^(1/6)`= 9 is ______


State whether the following statement is True or False: 

Order and degree of differential equation are always positive integers.


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


The order of the differential equation of all circles which lie in the first quadrant and touch both the axes 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 order of the differential equation whose general solution is given by `y=C_(1)e^(2x+C_2)+C_3e^x+C_4sin(x+C_5)` is ______.


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


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


The order and degree of the differential equation `(("d"^3y)/("d"x^3))^2 - 3 ("d"^2y)/("d"x^2) + 2(("d"y)/("d"x))^4` = y4 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 ______.


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


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?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×