Advertisements
Advertisements
प्रश्न
Determine the order and degree (if defined) of the differential equation:
`(d^4y)/(dx^4) + sin(y^("')) = 0`
Advertisements
उत्तर
`(d^4y)/(dx^4) + sin(y^(′′′)) = 0`
`=> y^(′′′) + sin(y^(′′′)) = 0`
The highest order derivative present in the differential equation is `y^(′′′)` . Therefore, its order is four.
The given differential equation is not a polynomial equation in its derivatives. Hence, its degree is not defined.
APPEARS IN
संबंधित प्रश्न
Write the degree of the differential equation `x^3((d^2y)/(dx^2))^2+x(dy/dx)^4=0`
Determine the order and degree (if defined) of the differential equation:
`(d^2y)/(dx^2)` = cos 3x + sin 3x
Determine the order and degree (if defined) of the differential equation:
y″ + 2y′ + sin y = 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`
(xy2 + x) dx + (y − x2y) dy = 0
(y'')2 + (y')3 + sin y = 0
Write the degree of the differential equation \[x^3 \left( \frac{d^2 y}{d x^2} \right)^2 + x \left( \frac{dy}{dx} \right)^4 = 0\]
Write the degree of the differential equation \[\frac{d^2 y}{d x^2} + 3 \left( \frac{dy}{dx} \right)^2 = x^2 \log\left( \frac{d^2 y}{d x^2} \right)\]
Write the degree of the differential equation \[\left( \frac{d^2 y}{d x^2} \right)^2 + \left( \frac{dy}{dx} \right)^2 = x\sin\left( \frac{dy}{dx} \right)\]
The degree of the differential equation \[\frac{d^2 y}{d x^2} + e^\frac{dy}{dx} = 0\]
The degree of the differential equation \[\left( \frac{d^2 y}{d x^2} \right)^2 - \left( \frac{dy}{dx} \right) = y^3\], 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
The order of the differential equation \[2 x^2 \frac{d^2 y}{d x^2} - 3\frac{dy}{dx} + y = 0\], is
Determine the order and degree (if defined) of the following differential equation:-
\[\left( \frac{ds}{dt} \right)^4 + 3s\frac{d^2 s}{d t^2} = 0\]
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:
`root(3)(1 +("dy"/"dx")^2) = ("d"^2"y")/"dx"^2`
Find the order and degree of the following differential equation:
`x+ dy/dx = 1 + (dy/dx)^2`
Order and degree of differential equation are always ______ integers
State whether the following statement is True or False:
Order and degree of differential equation `x ("d"^3y)/("d"x^3) + 6(("d"^2y)/("d"x^2))^2 + y` = 0 is (2, 2)
The order and degree of the differential equation `(dy/dx)^3 + ((d^3y)/dx^3) + xy = 0` are respectively ______
The degree of the differential equation `1/2 ("d"^3"y")/"dx"^3 = {1 + (("d"^2"y")/"dx"^2)}^(5/3)` is ______.
The order and degree of the differential equation `("d"^2"y")/"dx"^2 + (("d"^3"y")/"dx"^3) + x^(1/5) = 0` are respectively.
If m and n are the order and degree of the differential equation `((d^3y)/(dx^3))^6+5((d^3y)/(dx^3))^4/((d^4y)/(dx^4))+(d^4y)/(dx^4)=x^3-1,` then ______.
The order of the differential equation of all circles of given radius a 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 ______.
The order and degree of the differential equation `("d"^2y)/("d"x^2) + (("d"y)/("d"x))^(1/4) + x^(1/5)` = 0, respectively, are ______.
Write the sum of the order and the degree of the following differential equation:
`d/(dx) (dy/dx)` = 5
The order of differential equation `2x^2 (d^2y)/(dx^2) - 3 (dy)/(dx) + y` = 0 is
Write the degree of the differential equation (y''')2 + 3(y") + 3xy' + 5y = 0
The order of the differential equation of all parabolas, whose latus rectum is 4a and axis parallel to the x-axis, is ______.
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 ______.
Find the order and degree of the differential equation
`sqrt(1 + 1/(dy/dx)^2) = ((d^2y)/(dx^2))^(3/2)`
Find the order and degree of the differential equation `(d^2y)/(dx^2) = root(3)(1 - (dy/dx)^4`
