Advertisements
Advertisements
Question
The degree of the differential equation `[1 + (dy/dx)^2]^3 = ((d^2y)/(dx^2))^2` is ______.
Options
4
`3/2`
2
Not defined
Advertisements
Solution
The degree of the differential equation `[1 + (dy/dx)^2]^3 = ((d^2y)/(dx^2))^2` is 2.
APPEARS IN
RELATED QUESTIONS
Write the degree of the differential equation `x^3((d^2y)/(dx^2))^2+x(dy/dx)^4=0`
Determine the order and degree (if defined) of the differential equation:
y' + 5y = 0
Determine the order and degree (if defined) of the differential equation:
( y′′′) + (y″)3 + (y′)4 + y5 = 0
Determine the order and degree (if defined) of the differential equation:
y″ + (y′)2 + 2y = 0
(y'')2 + (y')3 + sin y = 0
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 = x sin x `xy'=y+xsqrt(x^2-y^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 equations.
`(d^2x)/(dt^2)+((dx)/(dt))^2 + 8=0`
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.
Find the order and degree of the following differential equation:
`x+ dy/dx = 1 + (dy/dx)^2`
Select and write the correct alternative from the given option for the question
The order and degree of `(("d"y)/("d"x))^3 - ("d"^3y)/("d"x^3) + y"e"^x` = 0 are respectively
Order of highest derivative occurring in the differential equation is called the ______ of the differential equation
State whether the following statement is True or False:
Order and degree of differential equation are always positive integers.
State whether the following statement is True or False:
The degree of a differential equation `"e"^(-("d"y)/("d"x)) = ("d"y)/("d"x) + "c"` is not defined
The order of the differential equation of all circles of given radius a is ______.
The degree of the differential equation `("dy"/"dx")^2 + (("d"^2y)/("d"x^2))^2` = 0 is ______.
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 ______.
The degree of the differential equation `sqrt(1 + (("d"y)/("d"x))^2)` = x is ______.
y2 = (x + c)3 is the general solution of the differential equation ______.
Determine the order and degree of the following differential equation:
`(d^2y)/(dx^2) + x((dy)/(dx)) + y` = 2 sin x
The order and the degree of the differential equation `(1 + 3 dy/dx)^2 = 4 (d^3y)/(dx^3)` respectively are ______.
Find the order and degree of the differential equation `(1 + 3 dy/dx)^(2/3) = 4((d^3y)/(dx^3))`.
Assertion: Degree of the differential equation: `a(dy/dx)^2 + bdx/dy = c`, is 3
Reason: If each term involving derivatives of a differential equation is a polynomial (or can be expressed as polynomial) then highest exponent of the highest order derivative is called the degree of the differential equation.
Which of the following is correct?
For the differential equation \[xy \frac{d^{2}y}{dx^{2}} + x \left( \frac{dy}{dx} \right)^{2} - y \frac{dy}{dx} = 0\], what is the degree?
Why is the degree of the differential equation \[y'' + \sin(y') = 0\] not defined?
