Advertisements
Advertisements
प्रश्न
Determine the order and degree (if defined) of the following differential equation:-
y"' + y2 + ey' = 0
Advertisements
उत्तर
y"' + y2 + ey' = 0
The highest order derivative in the given equation is y''' and its power is 1.
Therefore, the given differential equation is of third order.
This equation cannot be expressed as a polynomial of derivative.
Thus, the degree is not defined.
i.e., Order = 3 and degree is not defined.
APPEARS IN
संबंधित प्रश्न
Determine the order and degree (if defined) of the differential equation:
`(d^2y)/(dx^2)^2 + cos(dy/dx) = 0`
Determine the order and degree (if defined) of the differential equation:
( y′′′) + (y″)3 + (y′)4 + y5 = 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).
`(d^2y)/dx^2 + 5x(dy/dx)^2 - 6y = log x`
Write the degree of the differential equation
\[a^2 \frac{d^2 y}{d x^2} = \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^{1/4}\]
Write the order of the differential equation
\[1 + \left( \frac{dy}{dx} \right)^2 = 7 \left( \frac{d^2 y}{d x^2} \right)^3\]
What is the degree of the following differential equation?
Write the degree of the differential equation \[\left( \frac{dy}{dx} \right)^4 + 3x\frac{d^2 y}{d x^2} = 0\]
Write the degree of the differential equation x \[\left( \frac{d^2 y}{d x^2} \right)^3 + y \left( \frac{dy}{dx} \right)^4 + x^3 = 0\]
The order of the differential equation whose general solution is given by y = c1 cos (2x + c2) − (c3 + c4) ax + c5 + c6 sin (x − c7) 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:-
\[\left( \frac{ds}{dt} \right)^4 + 3s\frac{d^2 s}{d t^2} = 0\]
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
Write the order and degree of the differential equation `((d^4"y")/(d"x"^4))^2 = [ "x" + ((d"y")/(d"x"))^2]^3`.
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)^2 + cos ("dy"/"dx") = 0`
Determine the order and degree of the following differential equations.
`(y''')^2 + 2(y'')^2 + 6y' + 7y = 0`
Choose the correct alternative.
The order and degree of `(dy/dx)^3 - (d^3y)/dx^3 + ye^x = 0` are respectively.
Find the order and degree of the following differential equation:
`[ (d^3y)/dx^3 + x]^(3/2) = (d^2y)/dx^2`
Select and write the correct alternative from the given option for the question
The order and degree of `(1 + (("d"y)/("d"x))^3)^(2/3) = 8 ("d"^3y)/("d"x^3)` are respectively
Order and degree of differential equation`(("d"^3y)/("d"x^3))^(1/6)`= 9 is ______
State whether the following statement is True or False:
Order and degree of differential equation are always positive integers.
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 differential equation of the family of curves y = ex (A cos x + B sin x). Where A and B are arbitary constants 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.
The degree of the differential equation `[1 + (("d"y)/("d"x))^2]^(3/2) = ("d"^2y)/("d"x^2)` is ______.
The order and degree of the differential equation `[1 + ((dy)/(dx))^2] = (d^2y)/(dx^2)` are ______.
The degree of the differential equation `sqrt(1 + (("d"y)/("d"x))^2)` = x is ______.
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
If m and n, respectively, are the order and the degree of the differential equation `d/(dx) [((dy)/(dx))]^4` = 0, then m + n = ______.
Degree of the differential equation `sinx + cos(dy/dx)` = y2 is ______.
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`.
