Advertisements
Advertisements
प्रश्न
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.
पर्याय
True
False
Advertisements
उत्तर
The order of highest derivative occurring in the differential equation is called degree of the differential equation. - False
APPEARS IN
संबंधित प्रश्न
Determine the order and degree (if defined) of the differential equation:
`((ds)/(dt))^4 + 3s (d^2s)/(dt^2) = 0`
Determine the order and degree (if defined) of the differential equation:
( y′′′) + (y″)3 + (y′)4 + y5 = 0
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 degree of the differential equation \[x^3 \left( \frac{d^2 y}{d x^2} \right)^2 + x \left( \frac{dy}{dx} \right)^4 = 0\]
The degree of the differential equation \[\frac{d^2 y}{d x^2} + e^\frac{dy}{dx} = 0\]
The degree of the differential equation \[\left( \frac{d^2 y}{d x^2} \right)^2 - \left( \frac{dy}{dx} \right) = y^3\], is
Determine the order and degree (if defined) of the following differential equation:-
y"' + 2y" + y' = 0
In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-
`y=sqrt(1+x^2)` `y'=(xy)/(1+x^2)`
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:
`(("d"^2"y")/"dx"^2)^2 + cos ("dy"/"dx") = 0`
Determine the order and degree of the following differential equation:
`[1 + (dy/dx)^2]^(3/2) = 8(d^2y)/dx^2`
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.
`sqrt(1+1/(dy/dx)^2) = (dy/dx)^(3/2)`
Determine the order and degree of the following differential equations.
`((d^3y)/dx^3)^(1/6) = 9`
Choose the correct alternative:
The order and degree of `(1 + (("d"y)/("d"x))^3)^(2/3) = 8 ("d"^3y)/("d"x^3)` are respectively
The power of highest ordered derivative when all the derivatives are made free from negative and/or fractional indices if any is called ______ of the differential equation
Order of highest derivative occurring in the differential equation is called the degree of the differential equation
The degree of the differential equation `("d"^4"y")/"dx"^4 + sqrt(1 + ("dy"/"dx")^4)` = 0 is
The differential equation `x((d^2y)/dx^2)^3 + ((d^3y)/dx^3)^2y = x^2` is of ______
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 sum of the order and the degree of the following differential equation:
`d/(dx) (dy/dx)` = 5
If m and n, respectively, are the order and the degree of the differential equation `d/(dx) [((dy)/(dx))]^4` = 0, then m + n = ______.
The order of the differential equation of all parabolas, whose latus rectum is 4a and axis parallel to the x-axis, is ______.
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 ______.
Find the order and degree of the differential equation `(1 + 3 dy/dx)^(2/3) = 4((d^3y)/(dx^3))`.
For the differential equation \[y''' + y^{2} + e^{y'} = 0\], is the degree defined?
