Advertisements
Advertisements
Question
For the differential equation given below, indicate its order and degree (if defined).
`(d^2y)/dx^2 + 5x(dy/dx)^2 - 6y = log x`
Advertisements
Solution
`(d^2y)/dx^2 + 5x(dy/dx)^2 - 6y = log x`
In this differential equation, the highest derivative order is `(d^2y)/dx^2.`
Therefore, the order of the equation is 2, and the Degree is 1.
APPEARS IN
RELATED QUESTIONS
Determine the order and degree (if defined) of the differential equation:
y′ + y = ex
For the differential equation given below, indicate its order and degree (if defined).
`(d^4y)/dx^4 - sin ((d^3y)/(dx^3)) = 0`
For the given below, verify that the given function (implicit or explicit) is a solution to the corresponding differential equation.
xy = a ex + b e-x + x2 : `x (d^2y)/(dx^2) + 2 dy/dx - xy + x^2 - 2 = 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 order and degree of the differential equation
\[y = x\frac{dy}{dx} + a\sqrt{1 + \left( \frac{dy}{dx} \right)^2}\]
Write the degree of the differential equation
\[\frac{d^2 y}{d x^2} + x \left( \frac{dy}{dx} \right)^2 = 2 x^2 \log \left( \frac{d^2 y}{d x^2} \right)\]
Write the order of the differential equation of the family of circles touching X-axis at the origin.
Write the order of the differential equation of all non-horizontal lines in a plane.
What is the degree of the following differential equation?
The degree of the differential equation \[\left( \frac{d^2 y}{d x^2} \right)^3 + \left( \frac{dy}{dx} \right)^2 + \sin\left( \frac{dy}{dx} \right) + 1 = 0\], is
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 = cos x + C y' + sin x = 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)^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 equation:
`(("d"^3"y")/"dx"^3)^2 = root(5)(1 + "dy"/"dx")`
Determine the order and degree of the following differential equations.
`dy/dx = 7 (d^2y)/dx^2`
Fill in the blank:
The order of highest derivative occurring in the differential equation is called ___________ 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
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
Degree of the given differential equation
`(("d"^3"y")/"dx"^2)^2 = (1 + "dy"/"dx")^(1/3)` is
The order and degree of the differential equation `[1 + 1/("dy"/"dx")^2]^(5/3) = 5 ("d"^2y)/"dx"^2` are respectively.
The degree of the differential equation `1/2 ("d"^3"y")/"dx"^3 = {1 + (("d"^2"y")/"dx"^2)}^(5/3)` is ______.
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 ______.
The degree of the differential equation `("d"^2y)/("d"x^2) + 3("dy"/"dx")^2 = x^2 log(("d"^2y)/("d"x^2))` is ______.
The degree of the differential equation `("dy"/"dx")^2 + (("d"^2y)/("d"x^2))^2` = 0 is ______.
Degree of the differential equation `sqrt(1 + ("d"^2y)/("d"x^2)) = x + "dy"/"dx"` is not defined.
The degree of the differential equation `(("d"^2y)/("d"x^2))^2 + (("d"y)/("d"x))^2 = xsin(("d"y)/("d"x))` is ______.
The degree of the differential equation `("d"^2y)/("d"x^2) + "e"^((dy)/(dx))` = 0 is ______.
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))`.
