Advertisements
Advertisements
प्रश्न
Determine the order and degree of the following differential equation:
`(dy)/(dx) = (2sin x + 3)/(dy/dx)`
Advertisements
उत्तर
The given Differential equation is
`(dy)/(dx) = (2sin x + 3)/((dy)/(dx))`
∴ `(dy/dx)^2` = 2 sin x + 3
This D.E. has highest order derivative `"dy"/"dx"` with power 2.
∴ The given D.E. is of order 1 and degree 2.
संबंधित प्रश्न
Determine the order and degree (if defined) of the differential equation:
y' + 5y = 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
The degree of the differential equation `((d^2y)/(dx^2))^3 + ((dy)/(dx))^2 + sin ((dy)/(dx)) + 1 = 0` is ______.
For the given below, verify that the given function (implicit or explicit) is a solution to the corresponding differential equation.
`y = xsin 3x : (d^2y)/(dx^2) + 9y - 6 cos 3x = 0`
Define degree of a differential equation.
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
\[1 + \left( \frac{dy}{dx} \right)^2 = 7 \left( \frac{d^2 y}{d x^2} \right)^3\]
Write the order of the differential equation whose solution is y = a cos x + b sin x + c e−x.
Write the degree of the differential equation \[\left( 1 + \frac{dy}{dx} \right)^3 = \left( \frac{d^2 y}{d x^2} \right)^2\]
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 order and degree of the differential equation
\[\frac{d^2 y}{d x^2} + \left( \frac{dy}{dx} \right)^\frac{1}{4} + x^\frac{1}{5} = 0\]
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' + sin y = 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 = x sin x `xy'=y+xsqrt(x^2-y^2)`
Determine the order and degree of the following differential equation:
(y''')2 + 3y'' + 3xy' + 5y = 0
Determine the order and degree of the following differential equation:
`"dy"/"dx" = 3"y" + root(4)(1 + 5 ("dy"/"dx")^2)`
Determine the order and degree of the following differential equation:
`("d"^4"y")/"dx"^4 + sin ("dy"/"dx") = 0`
Fill in the blank:
Order and degree of a differential equation are always __________ integers.
State whether the following is True or False:
The power of the highest ordered derivative when all the derivatives are made free from negative and / or fractional indices if any is called order of the differential equation.
Select and write the correct alternative from the given option for the question
The order and degree of `(("d"y)/("d"x))^3 - ("d"^3y)/("d"x^3) + y"e"^x` = 0 are respectively
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 is the power of highest ordered derivative when all the derivatives are made free from negative and/or fractional indices if any
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 order and degree of `(("n + 1")/"n")("d"^4"y")/"dx"^4 = ["n" + (("d"^2"y")/"dx"^2)^4]^(3//5)` are respectively.
The order of the differential equation whose general solution is given by `y=C_(1)e^(2x+C_2)+C_3e^x+C_4sin(x+C_5)` is ______.
The order of the differential equation of all circles of radius r, having centre on X-axis and passing through the origin is ______.
Order of the differential equation representing the family of ellipses having centre at origin and foci on x-axis is two.
Degree of the differential equation `sqrt(1 + ("d"^2y)/("d"x^2)) = x + "dy"/"dx"` is not defined.
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 `(("d"^3y)/("d"x^3))^2 - 3 ("d"^2y)/("d"x^2) + 2(("d"y)/("d"x))^4` = y4 are ______.
Write the degree of the differential equation (y''')2 + 3(y") + 3xy' + 5y = 0
The differential equation representing the family of curves y2 = `2c(x + sqrt(c))`, where c is a positive parameter, is of ______.
The sum of the order and the degree of the differential equation `d/dx[(dy/dx)^3]` is ______.
The order and the degree of the differential equation `(1 + 3 dy/dx)^2 = 4 (d^3y)/(dx^3)` respectively are ______.
If `(a + bx)e^(y/x)` = x then prove that `x(d^2y)/(dx^2) = (a/(a + bx))^2`.
Find the order and degree of the differential equation `(d^2y)/(dx^2) = root(3)(1 - (dy/dx)^4`
Find the order and degree of the differential equation `(1 + 3 dy/dx)^(2/3) = 4((d^3y)/(dx^3))`.
