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

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 fr - Mathematics and Statistics

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प्रश्न

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

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर
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उत्तर

True

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.8: Differential Equation and Applications - Q.3

संबंधित प्रश्‍न

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

y' + 5y = 0


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

xy = a ex + b e-x + x2 : `x (d^2y)/(dx^2) + 2 dy/dx - xy + x^2 - 2 = 0`


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

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


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

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

(y'')2 + (y')3 + sin y = 0


Define order of a differential equation.


Write the degree of the differential equation
\[a^2 \frac{d^2 y}{d x^2} = \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^{1/4}\]


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 all non-horizontal lines in a plane.


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


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

y = x sin x              `xy'=y+xsqrt(x^2-y^2)`


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:

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


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.


Order and degree of differential equation are always ______ integers


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 ______.


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 ______.


y2 = (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 = ______.


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


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


The sum of the order and the degree of the differential equation `d/dx[(dy/dx)^3]` is ______.


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


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