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**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

#### Options

True

False

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#### Solution

**True**

#### RELATED QUESTIONS

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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

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Determine order and degree(if defined) of differential equation `((ds)/(dt))^4 + 3s (d^2s)/(dt^2) = 0`

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

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

`x^2 = 2y^2 log y : (x^2 + y^2) dy/dx - xy = 0`

(xy^{2} + x) dx + (y − x^{2}y) dy = 0

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Write the degree of the differential equation

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\[1 + \left( \frac{dy}{dx} \right)^2 = 7 \left( \frac{d^2 y}{d x^2} \right)^3\]

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

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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

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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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`y=sqrt(1+x^2)` `y'=(xy)/(1+x^2)`

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:**

`("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:**

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**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:**

(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`

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`(("d"^3"y")/"dx"^3)^(1/2) - ("dy"/"dx")^(1/3) = 20`

**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.

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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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**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.

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

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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.

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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 ______

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Order and degree of differential equation are always positive integers.

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**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)

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The order of the differential equation of all circles of radius r, having centre on X-axis and passing through the origin is ______.

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

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

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

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y^{2} = (x + c)^{3} is the general solution of the differential equation ______.

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

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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))`.