Advertisements
Advertisements
Question
The differential equation `y ("d"y)/("d"x) + "c"` represents: ______.
Options
Family of hyperbolas
Family of parabolas
Family of ellipses
Family of circles
Solution
The differential equation `y ("d"y)/("d"x) + "c"` represents: Family of circles.
Explanation:
Given differential equation is `y ("d"y)/("d"x) + x` = c
⇒ `y ("d"y)/("d"x)` = c – x
⇒ ydy = (c – x)dx
∴ Integrating both sides, we get
`int y "d"y = int ("c" - x) "d"x`
⇒ `y^2/2 = "c"x - x^2/2 + "k"`
⇒ `x^2/2 + y^2/2 - "c"x` = k
⇒ x2 + y2 – 2cx = 2k which is a family of circles.
APPEARS IN
RELATED QUESTIONS
Form the differential equation of the family of circles touching the y-axis at the origin.
Which of the following differential equation has y = x as one of its particular solution?
A. `(d^2y)/(dx^2) - x^2 (dy)/(dx) + xy = x`
B. `(d^2y)/(dx^2) + x dy/dx + xy = x`
C. `(d^2y)/(dx^2) - x^2 dy/dx + xy = 0`
D. `(d^2y)/(dx^2) + x dy/dx + xy = 0`
For the curve y = 5x – 2x3, if x increases at the rate of 2 units/sec, then find the rate of change of the slope of the curve when x = 3
Form the differential equation of the family of curves represented by y2 = (x − c)3.
Form the differential equation from the following primitive where constants are arbitrary:
xy = a2
Form the differential equation corresponding to y2 − 2ay + x2 = a2 by eliminating a.
Form the differential equation corresponding to (x − a)2 + (y − b)2 = r2 by eliminating a and b.
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
x2 + y2 = a2
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
x2 − y2 = a2
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
x2 + (y − b)2 = 1
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
(x − a)2 − y2 = 1
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
y = eax
Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.
Find one-parameter families of solution curves of the following differential equation:-
\[x\frac{dy}{dx} - y = \left( x + 1 \right) e^{- x}\]
Find one-parameter families of solution curves of the following differential equation:-
\[\left( x \log x \right)\frac{dy}{dx} + y = \log x\]
Find one-parameter families of solution curves of the following differential equation:-
\[\frac{dy}{dx} - \frac{2xy}{1 + x^2} = x^2 + 2\]
Find one-parameter families of solution curves of the following differential equation:-
\[\frac{dy}{dx} \cos^2 x = \tan x - y\]
Write the differential equation representing family of curves y = mx, where m is arbitrary constant.
Form the differential equation of the family of hyperbolas having foci on x-axis and centre at the origin.
Find the area of the region bounded by the curves (x -1)2 + y2 = 1 and x2 + y2 = 1, using integration.
Form the differential equation of all circles which pass through origin and whose centres lie on y-axis.
Find the differential equation of system of concentric circles with centre (1, 2).
Family y = Ax + A3 of curves will correspond to a differential equation of order ______.
The curve for which the slope of the tangent at any point is equal to the ratio of the abcissa to the ordinate of the point is ______.
The differential equation representing the family of circles x2 + (y – a)2 = a2 will be of order two.
Find the equation of the curve at every point of which the tangent line has a slope of 2x:
From the differential equation of the family of circles touching the y-axis at origin
