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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

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#### Solution

**degree**

#### 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 y′′′ + 2y″ + y′ = 0

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

The order of the differential equation

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

**(A)** 2

**(B)** 1

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**(D)** not defined

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

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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

The order of the differential equation \[2 x^2 \frac{d^2 y}{d x^2} - 3\frac{dy}{dx} + y = 0\], is

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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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^{'}= 0

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

`("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:**

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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.

`((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.

**Choose the correct alternative.**

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

**Fill in the blank:**

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

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

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

**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 of highest derivative occurring in the differential equation is called the ______ 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: **

Order and degree of differential equation are always positive integers.

**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 order and degree of the differential equation `[1 + 1/("dy"/"dx")^2]^(5/3) = 5 ("d"^2y)/"dx"^2` are respectively.

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

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 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 ______.

Order of the differential equation representing the family of parabolas y^{2} = 4ax is ______.

Degree of the differential equation `sqrt(1 + ("d"^2y)/("d"x^2)) = x + "dy"/"dx"` is not defined.

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

The order and degree of the differential equation `("d"^2y)/("d"x^2) + (("d"y)/("d"x))^(1/4) + x^(1/5)` = 0, respectively, are ______.

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 `("d"^2y)/("d"x^2) + "e"^((dy)/(dx))` = 0 is ______.

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

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 ______.

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

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

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

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 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 degree of the differential equation `((d^2y)/dx^2)^2 + (dy/dx)^3` = a^{x} is 3.

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

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 `(1 + 3 dy/dx)^(2/3) = 4((d^3y)/(dx^3))`.