Advertisements
Advertisements
Question
Choose the correct alternative.
The order and degree of `[ 1+ (dy/dx)^3]^(2/3) = 8 (d^3y)/dx^3` are respectively.
Options
3, 1
1, 3
3, 3
1, 1
Advertisements
Solution
The order and degree of `[ 1+ (dy/dx)^3]^(2/3) = 8 (d^3y)/dx^3` are respectively - 3, 3
Explanation
`[ 1+ (dy/dx)^3]^(2/3) = 8 (d^3y)/dx^3`
Taking cube on both sides, we get
`[ 1+ (dy/dx)^3]^(2/3) = 8^3 ((d^3y)/dx^3)^3`
∴ By definition of order and degree,
Order : 3; Degree : 3
APPEARS IN
RELATED QUESTIONS
Determine the order and degree (if defined) of the differential equation:
y″ + (y′)2 + 2y = 0
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`
Write the order of the differential equation of the family of circles touching X-axis at the origin.
The order of the differential equation satisfying
\[\sqrt{1 - x^4} + \sqrt{1 - y^4} = a\left( x^2 - y^2 \right)\] is
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:-
\[\left( \frac{ds}{dt} \right)^4 + 3s\frac{d^2 s}{d t^2} = 0\]
Determine the order and degree (if defined) of the following differential equation:-
(y"')2 + (y")3 + (y')4 + y5 = 0
In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-
y = x sin x `xy'=y+xsqrt(x^2-y^2)`
Determine the order and degree of the following differential equation:
`root(3)(1 +("dy"/"dx")^2) = ("d"^2"y")/"dx"^2`
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 equation:
`"x" + ("d"^2"y")/"dx"^2 = sqrt(1 + (("d"^2"y")/"dx"^2)^2)`
Choose the correct alternative.
The order and degree of `(dy/dx)^3 - (d^3y)/dx^3 + ye^x = 0` are respectively.
The order and degree of `((dy)/(dx))^3 - (d^3y)/(dx^3) + ye^x` = 0 are ______.
Order and degree of differential equation are always ______ integers
The order and degree of the differential equation `[1 + ["dy"/"dx"]^3]^(7/3) = 7 (("d"^2"y")/"dx"^2)` are respectively.
The order and degree of the differential equation `[1 + 1/("dy"/"dx")^2]^(5/3) = 5 ("d"^2y)/"dx"^2` are respectively.
The order and degree of the differential equation `(dy/dx)^3 + ((d^3y)/dx^3) + xy = 0` are respectively ______
Order of the differential equation representing the family of parabolas y2 = 4ax 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 order and degree of the differential equation `sqrt(dy/dx) - 4 dy/dx - 7x` = 0 are ______.
The degree of the differential equation `((d^2y)/dx^2)^2 + (dy/dx)^3` = ax is 3.
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))`.
The sum of the degree and order of the differential equation \[\sqrt{\frac{\mathrm{d}^{2}y}{\mathrm{d}x^{2}}}=\sqrt[5]{\frac{\mathrm{d}y}{\mathrm{d}x}-5}\] is
