Advertisements
Advertisements
प्रश्न
Write the degree of the differential equation
\[a^2 \frac{d^2 y}{d x^2} = \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^{1/4}\]
Advertisements
उत्तर
We have,
\[ a^2 \frac{d^2 y}{d x^2} = \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^{1/4} \]
\[ \left\{ a^2 \frac{d^2 y}{d x^2} \right\}^4 = 1 + \left( \frac{dy}{dx} \right)^2 \]
Degree of the differential equation is the degree of the highest order derivative .
Therefore, the degree must be 4 .
APPEARS IN
संबंधित प्रश्न
For the differential equation given below, indicate its order and degree (if defined).
`(d^2y)/dx^2 + 5x(dy/dx)^2 - 6y = log x`
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.
`x^2 = 2y^2 log y : (x^2 + y^2) dy/dx - xy = 0`
(xy2 + x) dx + (y − x2y) dy = 0
Write the order of the differential equation of the family of circles touching X-axis at the origin.
What is the degree of the following differential equation?
Write the degree of the differential equation x \[\left( \frac{d^2 y}{d x^2} \right)^3 + y \left( \frac{dy}{dx} \right)^4 + x^3 = 0\]
The degree of the differential equation \[\left( \frac{d^2 y}{d x^2} \right)^2 - \left( \frac{dy}{dx} \right) = y^3\], is
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
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:
`root(3)(1 +("dy"/"dx")^2) = ("d"^2"y")/"dx"^2`
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 equations.
`(y''')^2 + 2(y'')^2 + 6y' + 7y = 0`
Determine the order and degree of the following differential equations.
`sqrt(1+1/(dy/dx)^2) = (dy/dx)^(3/2)`
Find the order and degree of the following differential equation:
`[ (d^3y)/dx^3 + x]^(3/2) = (d^2y)/dx^2`
Order of highest derivative occurring in the differential equation is called the ______ of the differential equation
Order and degree of differential equation are always ______ integers
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 of the family of curves y = ex (A cos x + B sin x). Where A and B are arbitary constants is ______.
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 `("dy"/"dx")^2 + (("d"^2y)/("d"x^2))^2` = 0 is ______.
The degree of the differential equation `sqrt(1 + (("d"y)/("d"x))^2)` = x is ______.
Write the sum of the order and the degree of the following differential equation:
`d/(dx) (dy/dx)` = 5
The degree of differential equation `((d^2y)/(dx^2))^3 + ((dy)/(dx))^2 + sin((dy)/(dx)) + 1` = 0 is:
y2 = (x + c)3 is the general solution of the differential equation ______.
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 differential equation representing the family of curves y2 = `2c(x + sqrt(c))`, where c is a positive parameter, is of ______.
Degree of the differential equation `sinx + cos(dy/dx)` = y2 is ______.
The order and the degree of the differential equation `(1 + 3 dy/dx)^2 = 4 (d^3y)/(dx^3)` respectively are ______.
The degree of the differential equation `[1 + (dy/dx)^2]^3 = ((d^2y)/(dx^2))^2` is ______.
