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

State whether the following is True or False: The power of the highest ordered derivative when all the derivatives are made free from negative

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प्रश्न

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.

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर
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उत्तर

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. - False

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 8: Differential Equation and Applications - Miscellaneous Exercise 8 [पृष्ठ १७२]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 8 Differential Equation and Applications
Miscellaneous Exercise 8 | Q 3.5 | पृष्ठ १७२

संबंधित प्रश्‍न

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

( y′′′) + (y″)3 + (y′)4 + y5 = 0


\[s^2 \frac{d^2 t}{d s^2} + st\frac{dt}{ds} = s\]

\[5\frac{d^2 y}{d x^2} = \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^{3/2}\]

\[\frac{d^2 y}{d x^2} + 5x\left( \frac{dy}{dx} \right) - 6y = \log x\]

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

The degree of the differential equation \[\frac{d^2 y}{d x^2} + e^\frac{dy}{dx} = 0\]


Find the sum of the order and degree of the differential equation
\[y = x \left( \frac{dy}{dx} \right)^3 + \frac{d^2 y}{d x^2}\]


The degree of the differential equation \[\left( \frac{d^2 y}{d x^2} \right)^2 - \left( \frac{dy}{dx} \right) = y^3\], 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


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

y"' + 2y" + y' = 0


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

y" + 2y' + sin y = 0


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:

(y''')2 + 3y'' + 3xy' + 5y = 0


Determine the order and degree of the following differential equation:

`"x" + ("d"^2"y")/"dx"^2 = sqrt(1 + (("d"^2"y")/"dx"^2)^2)`


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:

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


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.


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


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


Degree of the given differential equation

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


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


y2 = (x + c)3 is the general solution of the differential equation ______.


Find the general solution of the following differential equation:

`(dy)/(dx) = e^(x-y) + x^2e^-y`


For the differential equation \[y''' + y^{2} + e^{y'} = 0\], what is the order?


Based on the differential equation illustrated with \[\left(\frac{d^{3}y}{dx^{3}}\right)^{2} + 5\frac{dy}{dx} = \sin(x)\], what is the order?


Which of the following statements is true regarding order and degree of differential equations?


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