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Order and degree of differential equation are always ______ integers - Mathematics and Statistics

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प्रश्न

Order and degree of differential equation are always ______ integers

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उत्तर

positive

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अध्याय 1.8: Differential Equation and Applications - Q.2

संबंधित प्रश्न

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^2y)/dx^2 + 5x(dy/dx)^2 - 6y = log x`


\[\frac{d^3 y}{d x^3} + \left( \frac{d^2 y}{d x^2} \right)^3 + \frac{dy}{dx} + 4y = \sin x\]

(y'')2 + (y')3 + sin y = 0


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

Write the order of the differential equation of all non-horizontal lines in a plane.


What is the degree of the following differential equation?

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

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


The order of the differential equation satisfying
\[\sqrt{1 - x^4} + \sqrt{1 - y^4} = a\left( x^2 - y^2 \right)\] 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


Find the order and the degree of the differential equation `x^2 (d^2y)/(dx^2) = { 1 + (dy/dx)^2}^4`


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:

`(("d"^2"y")/"dx"^2)^2 + cos ("dy"/"dx") = 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:

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


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 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


State whether the following statement is True or False: 

Order and degree of differential equation are always positive integers.


The degree of the differential equation `1/2 ("d"^3"y")/"dx"^3 = {1 + (("d"^2"y")/"dx"^2)}^(5/3)` is ______.


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 `sqrt(1 + (("d"y)/("d"x))^2)` = x is ______.


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


Write the degree of the differential equation (y''')2 + 3(y") + 3xy' + 5y = 0


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


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


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


Find the order and degree of the differential equation `(1 + 3 dy/dx)^(2/3) = 4((d^3y)/(dx^3))`.


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