Advertisements
Advertisements
प्रश्न
The degree of the differential equation `[1 + (("d"y)/("d"x))^2]^(3/2) = ("d"^2y)/("d"x^2)` is ______.
विकल्प
4
`3/2`
not defined
2
उत्तर
The degree of the differential equation `[1 + (("d"y)/("d"x))^2]^(3/2) = ("d"^2y)/("d"x^2)` is 2.
Explanation:
The given differential equation is
`[1 + (("d"y)/("d"x))^2]^(3/2) = (("d"^2y)/("d"x^2))`
Squaring both sides, we have
`[ 1 + (("d"y)/("d"x))^2]^3 = (("d"^2y)/("d"x^2))^2`
So, the degree of the given differential equation is 2.
APPEARS IN
संबंधित प्रश्न
Determine the order and degree (if defined) of the differential equation:
`(d^4y)/(dx^4) + sin(y^("')) = 0`
Determine the order and degree (if defined) of the differential equation:
y″ + (y′)2 + 2y = 0
The degree of the differential equation `((d^2y)/(dx^2))^3 + ((dy)/(dx))^2 + sin ((dy)/(dx)) + 1 = 0` is ______.
The order of the differential equation `2x^2 (d^2y)/(dx^2) - 3 (dy)/(dx) + y = 0` is ______.
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 degree of the differential equation \[\left( 1 + \frac{dy}{dx} \right)^3 = \left( \frac{d^2 y}{d x^2} \right)^2\]
Find the sum of the order and degree of the differential equation
\[y = x \left( \frac{dy}{dx} \right)^3 + \frac{d^2 y}{d x^2}\]
Write the order and degree of the differential equation `((d^4"y")/(d"x"^4))^2 = [ "x" + ((d"y")/(d"x"))^2]^3`.
Determine the order and degree of the following differential equation:
`("d"^2"y")/"dx"^2 + ("dy"/"dx")^2 + 7"x" + 5 = 0`
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:
`("d"^4"y")/"dx"^4 + sin ("dy"/"dx") = 0`
Determine the order and degree of the following differential equations.
`(d^2x)/(dt^2)+((dx)/(dt))^2 + 8=0`
Determine the order and degree of the following differential equations.
`(d^4y)/dx^4 + [1+(dy/dx)^2]^3 = 0`
Determine the order and degree of the following differential equations.
`((d^3y)/dx^3)^(1/6) = 9`
Order and degree of a differential equation are always positive integers.
The order and degree of the differential equation `(dy/dx)^3 + ((d^3y)/dx^3) + xy = 0` are respectively ______
The order of the differential equation of all circles of radius r, having centre on X-axis and passing through the origin is ______.
The degree of the differential equation `("d"^2y)/("d"x^2) + (("d"y)/("d"x))^3 + 6y^5` = 0 is ______.
The order of the differential equation of all parabolas, whose latus rectum is 4a and axis parallel to the x-axis, is ______.
The order and degree of the differential eqµation whose general solution is given by `(d^2y)/(dx^2) + (dy/dx)^50` = In `((d^2y)/dx^2)` respectively, are ______.
The sum of the order and the degree of the differential equation `d/dx[(dy/dx)^3]` is ______.
The degree of the differential equation `[1 + (dy/dx)^2]^3 = ((d^2y)/(dx^2))^2` is ______.
