Advertisements
Advertisements
प्रश्न
Find the differential equation of system of concentric circles with centre (1, 2).
उत्तर
Family of concentric circles with centre (1, 2) and radius ‘r’ is (x – 1)2 + (y – 2)2 = r2
Differentiating both sides w.r.t., x we get
`2(x - 1) + 2(y - 2) "dy"/"dx"` = 0
⇒ `(x - 1) + (y - 2) "dy"/"dx"` = 0
Which is the required equation.
APPEARS IN
संबंधित प्रश्न
Form the differential equation of the family of circles touching the y-axis at the origin.
Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.
Show that the family of curves for which `dy/dx = (x^2+y^2)/(2x^2)` is given by x2 - y2 = cx
Form the differential equation from the following primitive where constants are arbitrary:
y2 = 4ax
Find the differential equation of the family of curves y = Ae2x + Be−2x, where A and B are arbitrary constants.
Find the differential equation of the family of curves, x = A cos nt + B sin nt, where A and B are arbitrary constants.
Form the differential equation corresponding to y2 = a (b − x2) by eliminating a and b.
Form the differential equation of the family of curves represented by the equation (a being the parameter):
(x − a)2 + 2y2 = a2
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
y2 = 4ax
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):
x2 + y2 = ax3
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:-
\[\frac{dy}{dx} - y = \cos 2x\]
Find one-parameter families of solution curves of the following differential equation:-
\[x\frac{dy}{dx} + y = x^4\]
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 order of the differential equation representing the family of curves y = ax + a3.
The differential equation which represents the family of curves y = eCx is
The family of curves in which the sub tangent at any point of a curve is double the abscissae, is given by
Form the differential equation representing the family of curves y = A sin x, by eliminating the arbitrary constant A.
Find the equation of a curve whose tangent at any point on it, different from origin, has slope `y + y/x`.
Find the equation of a curve passing through the point (1, 1) if the perpendicular distance of the origin from the normal at any point P(x, y) of the curve is equal to the distance of P from the x-axis.
Find the equation of a curve passing through origin if the slope of the tangent to the curve at any point (x, y) is equal to the square of the difference of the abcissa and ordinate of the point.
Family y = Ax + A3 of curves is represented by the differential equation of degree ______.
The differential equation `y ("d"y)/("d"x) + "c"` represents: ______.
The differential equation representing the family of circles x2 + (y – a)2 = a2 will be of order two.
Form the differential equation of family of circles having centre on y-axis and raduis 3 units
Form the differential equation of the family of hyperbola having foci on x-axis and centre at origin.
