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State the degree of differential equation ЁЭСТЁЭССтБвЁЭСж/ЁЭССтБвЁЭСе +ЁЭССтБвЁЭСж/ЁЭССтБвЁЭСе = x - Mathematics and Statistics

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

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Since the given differential equation cannot be expressed as a polynomial in differential coefficients, the degree is not defined.

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рдкрд╛рда 2.6: Differential Equations - Answer the following

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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


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


(xy2 + x) dx + (y − x2y) dy = 0


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

\[5\frac{d^2 y}{d x^2} = \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^{3/2}\]

\[y = px + \sqrt{a^2 p^2 + b^2},\text{ where p} = \frac{dy}{dx}\]

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

Define degree of a differential equation.


Write the order of the differential equation
\[1 + \left( \frac{dy}{dx} \right)^2 = 7 \left( \frac{d^2 y}{d x^2} \right)^3\]


Write the order of the differential equation whose solution is y = a cos x + b sin x + c e−x.


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


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


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:-

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


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 degree of the differential equation `((d^4"y")/(d"x"^4))^2 =  [ "x" + ((d"y")/(d"x"))^2]^3`.


Determine the order and degree of the following differential equation:

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


Determine the order and degree of the following differential equation:

`[1 + (dy/dx)^2]^(3/2) = 8(d^2y)/dx^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)`


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 equation:

`(("d"^3"y")/"dx"^3)^2 = root(5)(1 + "dy"/"dx")`


Determine the order and degree of the following differential equations.

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


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


The order and degree of `((dy)/(dx))^3 - (d^3y)/(dx^3) + ye^x` = 0 are ______.


Choose the correct alternative:

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.


The order of the differential equation of all circles which lie in the first quadrant and touch both the axes is ______.


The degree of the differential equation `1/2 ("d"^3"y")/"dx"^3 = {1 + (("d"^2"y")/"dx"^2)}^(5/3)` is ______.


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


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


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


Polio drops are delivered to 50 K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation `"dy"/"dx" = "k"(50 - "y")` where x denotes the number of weeks and y the number of children who have been given the drops.

State the order of the above given differential equation.


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


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


Find the general solution of the following differential equation:

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


Determine the order and degree of the following differential equation:

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


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


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


The degree and order of the differential equation `[1 + (dy/dx)^3]^(7/3) = 7((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.


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 `(d^2y)/(dx^2) = root(3)(1 - (dy/dx)^4`


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