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(Y'')2 + (Y')3 + Sin Y = 0 - Mathematics

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प्रश्न

(y'')2 + (y')3 + sin y = 0

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उत्तर

\[\left( y'' \right)^2 + \left( y' \right)^3 + \sin y = 0\]
In this differential equation, the order of the highest order derivative is 2 and its power is 2. So, the order of the differential equation is 2 and its degree is 2.
It is a non-linear differential equation, as its degree is 2, which is more than 1.
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पाठ 22: Differential Equations - Exercise 22.01 [पृष्ठ ५]

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आरडी शर्मा Mathematics [English] Class 12
पाठ 22 Differential Equations
Exercise 22.01 | Q 22 | पृष्ठ ५

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

Order and degree of the differential equation `[1+(dy/dx)^3]^(7/3)=7(d^2y)/(dx^2)` are respectively 

(A) 2, 3

(B) 3, 2

(C) 7, 2

(D) 3, 7


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

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


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

`(d^4y)/dx^4 - sin ((d^3y)/(dx^3)) = 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`


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

\[\frac{d^3 y}{d x^3} + \frac{d^2 y}{d x^2} + \frac{dy}{dx} + y \sin y = 0\]

Define degree of a differential equation.


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


The degree of the differential equation \[\left( \frac{d^2 y}{d x^2} \right)^2 - \left( \frac{dy}{dx} \right) = y^3\], is


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


The degree of the differential equation \[\left( \frac{d^2 y}{d x^2} \right)^3 + \left( \frac{dy}{dx} \right)^2 + \sin\left( \frac{dy}{dx} \right) + 1 = 0\], is


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


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(y"')2 + (y")3 + (y')4 + y5 = 0


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

y" + (y')2 + 2y = 0


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


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:

`("d"^2"y")/"dx"^2 + ("dy"/"dx")^2 + 7"x" + 5 = 0`


Determine the order and degree of the following differential equation:

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


Fill in the blank:

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


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 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

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


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 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 radius r, having centre on X-axis and passing through the origin is ______.


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


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


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


The degree of the differential equation `dy/dx - x = (y - x dy/dx)^-4` is ______.


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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

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