Advertisements
Advertisements
Question
Write the order of the differential equation of all non-horizontal lines in a plane.
Advertisements
Solution
The equation of the non - horizontal lines in a plane is
\[y = mx + c, \]
where m is the slope and c is the intercept on y - axis .
Differentiating with respect to x, we get
\[\frac{dy}{dx} = m\]
\[ \Rightarrow \frac{d^2 y}{d x^2} = 0\]
This is the required differential equation .
Here, we observe that the order of the required differential equation is 2 .
APPEARS IN
RELATED QUESTIONS
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 ______.
(xy2 + x) dx + (y − x2y) dy = 0
Define degree of a differential equation.
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
\[\frac{d^2 y}{d x^2} + x \left( \frac{dy}{dx} \right)^2 = 2 x^2 \log \left( \frac{d^2 y}{d x^2} \right)\]
What is the degree of the following differential equation?
The order of the differential equation satisfying
\[\sqrt{1 - x^4} + \sqrt{1 - y^4} = a\left( x^2 - y^2 \right)\] is
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
Write the sum of the order and degree of the differential equation
\[\left( \frac{d^2 y}{{dx}^2} \right)^2 + \left( \frac{dy}{dx} \right)^3 + x^4 = 0 .\]
Determine the order and degree (if defined) of the following differential equation:-
y" + (y')2 + 2y = 0
Write the order and the degree of the following differential equation: `"x"^3 ((d^2"y")/(d"x"^2))^2 + "x" ((d"y")/(d"x"))^4 = 0`
Determine the order and degree of the following differential equation:
`(dy)/(dx) = (2sin x + 3)/(dy/dx)`
Determine the order and degree of the following differential equation:
`("d"^2"y")/"dx"^2 + ("dy"/"dx")^2 + 7"x" + 5 = 0`
Choose the correct option from the given alternatives:
The order and degree of the differential equation `sqrt(1 + ("dy"/"dx")^2) = (("d"^2"y")/"dx"^2)^(3/2)` are respectively.
Determine the order and degree of the following differential equation:
`("d"^2"y")/"dx"^2 + 5 "dy"/"dx" + "y" = "x"^3`
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 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 the degree of differential equation `e^((dy)/(dx)) + (dy)/(dx)` = x
State whether the following statement is True or False:
The degree of a differential equation is the power of highest ordered derivative when all the derivatives are made free from negative and/or fractional indices if any
The differential equation `x((d^2y)/dx^2)^3 + ((d^3y)/dx^3)^2y = x^2` is of ______
The order and degree of `(("n + 1")/"n")("d"^4"y")/"dx"^4 = ["n" + (("d"^2"y")/"dx"^2)^4]^(3//5)` 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 ______.
Order of the differential equation representing the family of parabolas y2 = 4ax is ______.
The degree of the differential equation `[1 + (("d"y)/("d"x))^2]^(3/2) = ("d"^2y)/("d"x^2)` is ______.
The order and degree of the differential equation `[1 + ((dy)/(dx))^3]^(2/3) = 8((d^3y)/(dx^3))` are respectively ______.
Find the general solution of the following differential equation:
`(dy)/(dx) = e^(x-y) + x^2e^-y`
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?
