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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Select and write the correct alternative from the given option for the question The order and degree of (1+(dydx)3)23=8d3dx3 are respectively

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प्रश्न

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

पर्याय

  • 3, 1

  • 1, 3

  • 3, 3

  • 1, 1

MCQ
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उत्तर

3, 3

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पाठ 2.6: Differential Equations - MCQ

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

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:

`(d^2y)/(dx^2)` = cos 3x + sin 3x


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

y′ + y = ex


\[s^2 \frac{d^2 t}{d s^2} + st\frac{dt}{ds} = s\]

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

\[2\frac{d^2 y}{d x^2} + 3\sqrt{1 - \left( \frac{dy}{dx} \right)^2 - y} = 0\]

Define order of a differential equation.


Define degree of a differential equation.


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


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

 


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


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


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


Write the order and degree of the differential equation
\[\frac{d^2 y}{d x^2} + \left( \frac{dy}{dx} \right)^\frac{1}{4} + x^\frac{1}{5} = 0\]


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


If p and q are the order and degree of the differential equation \[y\frac{dy}{dx} + x^3 \frac{d^2 y}{d x^2} + xy\] = cos x, then


The order of the differential equation \[2 x^2 \frac{d^2 y}{d x^2} - 3\frac{dy}{dx} + y = 0\], 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"' + y2 + ey' = 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)`


Write the order and the degree of the following differential equation: `"x"^3 ((d^2"y")/(d"x"^2))^2 + "x" ((d"y")/(d"x"))^4 = 0`


Determine the order and degree of the following differential equation:

`(dy)/(dx) = (2sin x + 3)/(dy/dx)`


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:

(y''')2 + 3y'' + 3xy' + 5y = 0


Fill in the blank:

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


Fill in the blank:

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


State whether the following statement is true or false:

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


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

The order and degree of `(("d"y)/("d"x))^3 - ("d"^3y)/("d"x^3) + y"e"^x` = 0 are respectively


State whether the following statement is True or False: 

Order and degree of differential equation are always positive integers.


The order and degree of the differential equation `(dy/dx)^3 + ((d^3y)/dx^3) + xy = 0` are respectively ______


The order and degree of `(("n + 1")/"n")("d"^4"y")/"dx"^4 = ["n" + (("d"^2"y")/"dx"^2)^4]^(3//5)` are respectively.


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


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 `("d"^2y)/("d"x^2) + (("d"y)/("d"x))^3 + 6y^5` = 0 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 ______.


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

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


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


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


If m and n, respectively, are the order and the degree of the differential equation `d/(dx) [((dy)/(dx))]^4` = 0, then m + n = ______.


The differential equation representing the family of curves y2 = `2c(x + sqrt(c))`, where c is a positive parameter, is of ______.


The order of the differential equation of all parabolas, whose latus rectum is 4a and axis parallel to the x-axis, is ______.


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 the degree of the differential equation `(1 + 3 dy/dx)^2 = 4 (d^3y)/(dx^3)` respectively are ______.


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