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Order of highest derivative occurring in the differential equation is called the ______ of the differential equation

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#### Solution

**order**

#### 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^4y)/(dx^4) + sin(y^("')) = 0`

Determine order and degree(if defined) of differential equation

( y′′′) + (y″)^{3} + (y′)^{4} + y^{5} = 0

Determine order and degree(if defined) of differential equation y′′′ + 2y″ + y′ = 0

The order of the differential equation

`2x^2 (d^2y)/(dx^2) - 3 (dy)/(dx) + y = 0` is

**(A)** 2

**(B)** 1

**(C)** 0

**(D)** not defined

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

`((dy)/(dx))^3 -4(dy/dx)^2 + 7y = sin x`

For given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.

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

(xy^{2} + x) dx + (y − x^{2}y) dy = 0

(*y*'')^{2} + (*y*')^{3} + sin *y* = 0

Define order of a differential equation.

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

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

Write the order and degree of the differential equation

\[\frac{d^2 y}{d x^2} + \left( \frac{dy}{dx} \right)^\frac{1}{4} + x^\frac{1}{5} = 0\]

The degree of the differential equation \[\left\{ 5 + \left( \frac{dy}{dx} \right)^2 \right\}^{5/3} = x^5 \left( \frac{d^2 y}{d x^2} \right)\], is

The order of the differential equation whose general solution is given by y = c_{1} cos (2x + c_{2}) − (c_{3} + c_{4}) a^{x}^{ + c5} + c_{6} sin (x − c_{7}) is

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

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

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

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

*y* = *x*^{2} + 2*x* + *C y' − 2x − 2 = 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 + "x"("dy"/"dx")` + y = 2 sin x

**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:**

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

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

(y''')^{2} + 3y'' + 3xy' + 5y = 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:**

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

**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:**

`"x" + ("d"^2"y")/"dx"^2 = sqrt(1 + (("d"^2"y")/"dx"^2)^2)`

**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:**

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

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

`"dy"/"dx" = 3"y" + root(4)(1 + 5 ("dy"/"dx")^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^2x)/(dt^2)+((dx)/(dt))^2 + 8=0`

Determine the order and degree of the following differential equations.

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

Determine the order and degree of the following differential equations.

`sqrt(1+1/(dy/dx)^2) = (dy/dx)^(3/2)`

Determine the order and degree of the following differential equations.

`dy/dx = 7 (d^2y)/dx^2`

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 `(dy/dx)^3 - (d^3y)/dx^3 + ye^x = 0` are respectively.

**Fill in the blank:**

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

**Fill in the blank:**

The power of the highest ordered derivative when all the derivatives are made free from negative and / or fractional indices if any is called __________ of the differential equation.

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

**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**

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

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

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

Order and degree of differential equation are always ______ integers

The power of highest ordered derivative when all the derivatives are made free from negative and/or fractional indices if any is called ______ of the differential equation

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

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

The degree of a differential equation is the power of highest ordered derivative when all the derivatives are made free from negative and/or fractional indices if any

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

The degree of a differential equation `"e"^(-("d"y)/("d"x)) = ("d"y)/("d"x) + "c"` is not defined

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

Order and degree of differential equation `x ("d"^3y)/("d"x^3) + 6(("d"^2y)/("d"x^2))^2 + y` = 0 is (2, 2)

The degree of the differential equation `("d"^4"y")/"dx"^4 + sqrt(1 + ("dy"/"dx")^4)` = 0 is

The order of the differential equation of all circles whose radius is 4, is ______.

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 ______.

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

The differential equation of the family of curves y = e^{x} (A cos x + B sin x). Where A and B are arbitary constants 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 of the differential equation of all circles of given radius a 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` = y^{4} are ______.

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

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

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

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

y^{2} = (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 = ______.

**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 y^{2} = `2c(x + sqrt(c))`, where c is a positive parameter, is of ______.

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 degree of the differential equation `sqrt(dy/dx) - 4 dy/dx - 7x` = 0 are ______.

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

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

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

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))`.