Advertisements
Advertisements
Question
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`
Advertisements
Solution
Order is the highest order derivative present in the differential equation
And the degree is the power of the highest order derivative.
We have given the differential equation:
`"x"^3 ((d^2"y")/(d"x"^2))^2 + "x" ((d"y")/(d"x"))^4 = 0`
Here, order is 2 and degree is 2.
APPEARS IN
RELATED QUESTIONS
Determine the order and degree (if defined) of the differential equation:
`(d^2y)/(dx^2)^2 + cos(dy/dx) = 0`
The degree of the differential equation `((d^2y)/(dx^2))^3 + ((dy)/(dx))^2 + sin ((dy)/(dx)) + 1 = 0` is ______.
For the differential equation given below, indicate its order and degree (if defined).
`(d^2y)/dx^2 + 5x(dy/dx)^2 - 6y = log x`
For the differential equation given below, indicate its order and degree (if defined).
`(d^4y)/dx^4 - sin ((d^3y)/(dx^3)) = 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`
What is the degree of the following differential equation?
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 \[\left\{ 5 + \left( \frac{dy}{dx} \right)^2 \right\}^{5/3} = x^5 \left( \frac{d^2 y}{d x^2} \right)\], is
Determine the order and degree (if defined) of the following differential equation:-
y" + 2y' + sin 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:
`(("d"^3"y")/"dx"^3)^(1/2) - ("dy"/"dx")^(1/3) = 20`
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.
`sqrt(1+1/(dy/dx)^2) = (dy/dx)^(3/2)`
Fill in the blank:
Order and degree of a differential equation are always __________ integers.
State the degree of differential equation `e^((dy)/(dx)) + (dy)/(dx)` = x
Order and degree of differential equation`(("d"^3y)/("d"x^3))^(1/6)`= 9 is ______
The order of the differential equation of all circles whose radius is 4, is ______.
The degree of the differential equation `(1 + "dy"/"dx")^3 = (("d"^2y)/("d"x^2))^2` is ______.
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) + (("d"y)/("d"x))^3 + 6y^5` = 0 is ______.
Polio drops are delivered to 50 K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation `"dy"/"dx" = "k"(50 - "y")` where x denotes the number of weeks and y the number of children who have been given the drops.
State the order of the above given differential equation.
The differential equation representing the family of curves y2 = `2c(x + sqrt(c))`, where c is a positive parameter, is of ______.
