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Determine the order and degree of the following differential equations. d4ydx4+[1+(dydx)2]3 - Mathematics and Statistics

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प्रश्न

Determine the order and degree of the following differential equations.

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

बेरीज
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उत्तर

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

By definition of order and degree,

Order : 4 ; Degree : 1

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पाठ 8: Differential Equation and Applications - Exercise 8.1 [पृष्ठ १६२]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 8 Differential Equation and Applications
Exercise 8.1 | Q 1.3 | पृष्ठ १६२

संबंधित प्रश्‍न

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


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

Define degree of a differential equation.


Write the order and degree of the differential equation
\[y = x\frac{dy}{dx} + a\sqrt{1 + \left( \frac{dy}{dx} \right)^2}\]


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


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

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


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

y"' + 2y" + y' = 0


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")^2 + 7"x" + 5 = 0`


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:

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


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`


Fill in the blank:

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


Find the order and degree of the following differential equation:

`[ (d^3y)/dx^3 + x]^(3/2) = (d^2y)/dx^2`


Find the order and degree of the following differential equation:

`x+ dy/dx = 1 + (dy/dx)^2`


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


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


The order and degree of the differential equation `[1 + ["dy"/"dx"]^3]^(7/3) = 7 (("d"^2"y")/"dx"^2)` are respectively.


The differential equation `x((d^2y)/dx^2)^3 + ((d^3y)/dx^3)^2y = x^2` is of ______ 


The order and degree of the differential equation `("d"^2"y")/"dx"^2 + (("d"^3"y")/"dx"^3) + x^(1/5) = 0` are respectively.


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


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


Assertion: Degree of the differential equation: `a(dy/dx)^2 + bdx/dy = c`, is 3

Reason: If each term involving derivatives of a differential equation is a polynomial (or can be expressed as polynomial) then highest exponent of the highest order derivative is called the degree of the differential equation.

Which of the following is correct?


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