Advertisements
Advertisements
प्रश्न
Write the order and degree of the differential equation `((d^4"y")/(d"x"^4))^2 = [ "x" + ((d"y")/(d"x"))^2]^3`.
उत्तर
Since,
The given differential equation is
`((d^4"y")/(d"x"^4))^2 = [ "x" + ((d"y")/(d"x"))^2]^3`
`((d^4"y")/(d"x"^4))^2 = "x"^3 + ((d"y")/(d"x"))^6 + 3"x"^2 ((d"y")/(d"x"))^2 + 3"x" ((d"y")/(d"x"))^4`
The highest order derivative in the differential equation is `(d^4"y")/(d"x"^4)` ⇒ Order of the given differential equation is 4.
The highest power raised to `(d^4"y")/(d"x"^4)` is 2⇒ Degree of the given differential equation is 2.
APPEARS IN
संबंधित प्रश्न
Determine the order and degree (if defined) of the differential equation:
`(d^2y)/(dx^2)` = cos 3x + sin 3x
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.
`y = xsin 3x : (d^2y)/(dx^2) + 9y - 6 cos 3x = 0`
(y'')2 + (y')3 + sin y = 0
Write the degree of the differential equation \[x^3 \left( \frac{d^2 y}{d x^2} \right)^2 + x \left( \frac{dy}{dx} \right)^4 = 0\]
Write the degree of the differential equation \[\frac{d^2 y}{d x^2} + 3 \left( \frac{dy}{dx} \right)^2 = x^2 \log\left( \frac{d^2 y}{d x^2} \right)\]
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
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
Write the sum of the order and degree of the differential equation
\[\left( \frac{d^2 y}{{dx}^2} \right)^2 + \left( \frac{dy}{dx} \right)^3 + x^4 = 0 .\]
Determine the order and degree (if defined) of the following differential equation:-
(y"')2 + (y")3 + (y')4 + y5 = 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"^2"y")/"dx"^2 + "dy"/"dx" + "x" = sqrt(1 + ("d"^3"y")/"dx"^3)`
Determine the order and degree of the following differential equation:
(y''')2 + 3y'' + 3xy' + 5y = 0
State whether the following is True or False:
The order of highest derivative occurring in the differential equation is called degree of the differential equation.
State whether the following is True or False:
The degree of the differential equation `e^((dy)/(dx)) = dy/dx +c` is not defined.
State the degree of differential equation `"e"^((dy)/(dx)) + (dy)/(dx)` = x
The order and degree of `((dy)/(dx))^3 - (d^3y)/(dx^3) + ye^x` = 0 are ______.
Order of highest derivative occurring in the differential equation is called the degree of the differential equation
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 ______.
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.
Find the general solution of the following differential equation:
`(dy)/(dx) = e^(x-y) + x^2e^-y`
The degree and order of the differential equation `[1 + (dy/dx)^3]^(7/3) = 7((d^2y)/(dx^2))` respectively are ______.
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`.
Find the order and degree of the differential equation `(1 + 3 dy/dx)^(2/3) = 4((d^3y)/(dx^3))`.
