Advertisements
Advertisements
प्रश्न
Write the degree of the differential equation \[\left( \frac{d^2 y}{d x^2} \right)^2 + \left( \frac{dy}{dx} \right)^2 = x\sin\left( \frac{dy}{dx} \right)\]
उत्तर
The given differential equation is not a polynomial equation in derivatives.
Hence, the degree for this differential equation is not defined.
APPEARS IN
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
Determine the order and degree (if defined) of the differential equation:
y′ + y = ex
For the differential equation given below, indicate its order and degree (if defined).
`((dy)/(dx))^3 -4(dy/dx)^2 + 7y = sin x`
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 = e^x (acos x + b sin x) : (d^2y)/(dx^2) - 2 dy/dx + 2y = 0`
Define degree of a differential equation.
Write the order of the differential equation of the family of circles touching X-axis at the origin.
Write the order of the differential equation of all non-horizontal lines in a plane.
The degree of the differential equation \[\frac{d^2 y}{d x^2} + e^\frac{dy}{dx} = 0\]
The degree of the differential equation \[\left\{ 5 + \left( \frac{dy}{dx} \right)^2 \right\}^{5/3} = x^5 \left( \frac{d^2 y}{d x^2} \right)\], is
The order of the differential equation satisfying
\[\sqrt{1 - x^4} + \sqrt{1 - y^4} = a\left( x^2 - y^2 \right)\] is
Write the sum of the order and degree of the differential equation
\[\left( \frac{d^2 y}{{dx}^2} \right)^2 + \left( \frac{dy}{dx} \right)^3 + x^4 = 0 .\]
Determine the order and degree (if defined) of the following differential equation:-
\[\left( \frac{ds}{dt} \right)^4 + 3s\frac{d^2 s}{d t^2} = 0\]
Determine the order and degree (if defined) of the following differential equation:-
(y"')2 + (y")3 + (y')4 + y5 = 0
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:
`(dy)/(dx) = (2sin x + 3)/(dy/dx)`
Determine the order and degree of the following differential equation:
`("d"^2"y")/"dx"^2 + "dy"/"dx" + "x" = sqrt(1 + ("d"^3"y")/"dx"^3)`
Determine the order and degree of the following differential equation:
`("d"^2"y")/"dx"^2 + 5 "dy"/"dx" + "y" = "x"^3`
Choose the correct alternative.
The order and degree of `(dy/dx)^3 - (d^3y)/dx^3 + ye^x = 0` are respectively.
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 ______.
State whether the following statement is True or False:
The degree of a differential equation `"e"^(-("d"y)/("d"x)) = ("d"y)/("d"x) + "c"` is not defined
The order of the differential equation of all circles of radius r, having centre on X-axis and passing through the origin is ______.
The degree of the differential equation `("d"^2y)/("d"x^2) + 3("dy"/"dx")^2 = x^2 log(("d"^2y)/("d"x^2))` is ______.
The order and degree of the differential equation `[1 + ("dy"/"dx")^2]^2 = ("d"^2y)/("d"x^2)` respectively, are ______.
The order of the differential equation of all circles of given radius a is ______.
Order of the differential equation representing the family of ellipses having centre at origin and foci on x-axis is two.
The degree of the differential equation `(("d"^2y)/("d"x^2))^2 + (("d"y)/("d"x))^2 = xsin(("d"y)/("d"x))` is ______.
The degree of the differential equation `("d"^2y)/("d"x^2) + "e"^((dy)/(dx))` = 0 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:
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 differential equation representing the family of curves y2 = `2c(x + sqrt(c))`, where c is a positive parameter, is of ______.
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 ______.