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

Choose the correct alternative: The order and degree of (1+(ddx)3)23=8d3ydx3 are respectively - Mathematics and Statistics

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प्रश्न

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

पर्याय

  • 3, 1

  • 1, 3

  • 3, 3

  • 1, 1

MCQ
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उत्तर

3, 3 

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पाठ 1.8: Differential Equation and Applications - Q.1

संबंधित प्रश्‍न

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

`(d^4y)/(dx^4) + sin(y^("')) = 0`


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

y' + 5y = 0


For the differential equation given below, indicate its order and degree (if defined).

`(d^4y)/dx^4 - sin ((d^3y)/(dx^3)) = 0`


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

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

\[e^\frac{dy}{dx} = x + 1 ; y\left( 0 \right) = 3\]

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

y" + (y')2 + 2y = 0


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

y = x2 + 2x + C            y' − 2x − 2 = 0


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

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


Write the order and the degree of the following differential equation: `"x"^3 ((d^2"y")/(d"x"^2))^2 + "x" ((d"y")/(d"x"))^4 = 0`


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:

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


Fill in the blank:

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


State whether the following statement is true or false:

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


The order and degree of `((dy)/(dx))^3 - (d^3y)/(dx^3) + ye^x` = 0 are ______.


Order and degree of differential equation`(("d"^3y)/("d"x^3))^(1/6)`= 9 is ______


The order and degree of the differential equation `[1 + ["dy"/"dx"]^3]^(7/3) = 7 (("d"^2"y")/"dx"^2)` 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 `("dy"/"dx")^2 + (("d"^2y)/("d"x^2))^2` = 0 is ______.


Degree of the differential equation `sqrt(1 + ("d"^2y)/("d"x^2)) = x + "dy"/"dx"` is not defined.


Polio drops are delivered to 50 K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation `"dy"/"dx" = "k"(50 - "y")` where x denotes the number of weeks and y the number of children who have been given the drops.

State the order of the above given differential equation.


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


Find the general solution of the following differential equation:

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


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


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


If `(a + bx)e^(y/x)` = x then prove that `x(d^2y)/(dx^2) = (a/(a + bx))^2`.


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


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