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महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

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

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प्रश्न

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

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर
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उत्तर

This statement is False.

Explanation:

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

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पाठ 1.8: Differential Equation and Applications - Q.3

संबंधित प्रश्‍न

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


\[y = px + \sqrt{a^2 p^2 + b^2},\text{ where p} = \frac{dy}{dx}\]

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 order of the differential equation of the family of circles touching X-axis at the origin.


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


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

y" + (y')2 + 2y = 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 equations.

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


Determine the order and degree of the following differential equations.

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


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 ______


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


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


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


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 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 ______.


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


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


The degree of the differential equation `("d"^2y)/("d"x^2) + (("d"y)/("d"x))^3 + 6y^5` = 0 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` = y4 are ______.


Write the sum of the order and the degree of the following differential equation:

`d/(dx) (dy/dx)` = 5


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


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 ______.


Degree of the differential equation `sinx + cos(dy/dx)` = y2 is ______.


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 `((d^3y)/(dx^2))^4 + ((d^2y)/(dx^2))^5 + (dy)/(dx) + y = 0` is ______.


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