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**State whether the following statement is True or False: **

Order and degree of differential equation are always positive integers.

#### Options

True

False

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#### Solution

**True**

#### APPEARS IN

#### RELATED QUESTIONS

Write the degree of the differential equation `x^3((d^2y)/(dx^2))^2+x(dy/dx)^4=0`

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 order and degree(if defined) of differential equation `(d^2y)/(dx^2)` = cos 3x + sin 3x

Determine order and degree(if defined) of differential equation y′ + y = e^{x}

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The order of the differential equation

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**(A)** 2

**(B)** 1

**(C)** 0

**(D)** not defined

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

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Define order of a differential equation.

Define degree of a differential equation.

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

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The degree of the differential equation \[\frac{d^2 y}{d x^2} + e^\frac{dy}{dx} = 0\]

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

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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

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

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

(*y*"')^{2} + (*y*")^{3} + (*y*')^{4} + *y*^{5} = 0

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

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

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

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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:**

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**Determine the order and degree of the following differential equation:**

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

**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:**

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**Determine the order and degree of the following differential equation:**

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**Determine the order and degree of the following differential equation:**

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**Determine the order and degree of the following differential equation:**

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**Determine the order and degree of the following differential equation:**

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**Choose the correct option from the given alternatives:**

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

**Determine the order and degree of the following differential equation:**

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**Determine the order and degree of the following differential equation:**

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**Determine the order and degree of the following differential equation:**

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Determine the order and degree of the following differential equations.

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Determine the order and degree of the following differential equations.

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**Fill in the blank:**

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

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

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

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

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

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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 2^{nd} week half the children have been given the polio drops. How many will have been given the drops by the end of 3^{rd} 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:

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

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

Write the degree of the differential equation (y''')^{2} + 3(y") + 3xy' + 5y = 0

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

Find the order and degree of the differential equation

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

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