Advertisements
Advertisements
प्रश्न
Determine the order and degree (if defined) of the differential equation:
y′′′ + 2y″ + y′ = 0
Advertisements
उत्तर
y′′′ + 2y″ + y′ = 0
The highest-order derivative is y′′′, which has a degree of 2.
Thus, the provided differential equation has order 3 and degree 2.
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:
y′ + y = ex
Determine the order and degree (if defined) of the differential equation:
y″ + (y′)2 + 2y = 0
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`
Define order of a differential equation.
Write the order of the differential equation of all non-horizontal lines in a plane.
The degree of the differential equation \[\left( \frac{d^2 y}{d x^2} \right)^3 + \left( \frac{dy}{dx} \right)^2 + \sin\left( \frac{dy}{dx} \right) + 1 = 0\], is
Determine the order and degree (if defined) of the following differential equation:-
\[\left( \frac{ds}{dt} \right)^4 + 3s\frac{d^2 s}{d t^2} = 0\]
Determine the order and degree (if defined) of the following differential equation:-
(y"')2 + (y")3 + (y')4 + y5 = 0
Determine the order and degree (if defined) of the following differential equation:-
y"' + 2y" + y' = 0
Determine the order and degree (if defined) of the following differential equation:-
y"' + y2 + ey' = 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 = cos x + C y' + sin x = 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)`
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`
Determine the order and degree of the following differential equation:
`(("d"^3"y")/"dx"^3)^2 = root(5)(1 + "dy"/"dx")`
Determine the order and degree of the following differential equations.
`(y''')^2 + 2(y'')^2 + 6y' + 7y = 0`
Determine the order and degree of the following differential equations.
`dy/dx = 7 (d^2y)/dx^2`
Choose the correct alternative.
The order and degree of `[ 1+ (dy/dx)^3]^(2/3) = 8 (d^3y)/dx^3` are respectively.
Fill in the blank:
The power of the highest ordered derivative when all the derivatives are made free from negative and / or fractional indices if any is called __________ of the differential equation.
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
State the degree of differential equation `e^((dy)/(dx)) + (dy)/(dx)` = x
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
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
Order and degree of differential equation`(("d"^3y)/("d"x^3))^(1/6)`= 9 is ______
Order of highest derivative occurring in the differential equation is called the degree of the differential equation
The degree of the differential equation `("d"^4"y")/"dx"^4 + sqrt(1 + ("dy"/"dx")^4)` = 0 is
The degree of the differential equation `1/2 ("d"^3"y")/"dx"^3 = {1 + (("d"^2"y")/"dx"^2)}^(5/3)` is ______.
Degree of the differential equation `sqrt(1 + ("d"^2y)/("d"x^2)) = x + "dy"/"dx"` is not defined.
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 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 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 `(1 + 3 dy/dx)^(2/3) = 4((d^3y)/(dx^3))`.
What is the fundamental condition required for the degree of a differential equation to be defined?
What is the key difference between order and degree of a differential equation?
