Advertisements
Advertisements
Question
Find the differential equation of the family of lines through the origin.
Advertisements
Solution
Let y = mx be the family of lines through origin.
Therefore, `"dy"/"dx"` = m
Eliminating m,
We get y = `"dy"/"dx" * x` or `x "dy"/"dx" - y` = 0.
APPEARS IN
RELATED QUESTIONS
Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.
Form the differential equation of the family of hyperbolas having foci on x-axis and centre at origin.
Form the differential equation of the family of circles having centre on y-axis and radius 3 units.
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:
y = cx + 2c2 + c3
Form the differential equation corresponding to y2 = a (b − x2) by eliminating a and b.
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):
y2 = 4a (x − b)
Find one-parameter families of solution curves of the following differential equation:-
\[\frac{dy}{dx} + 3y = e^{mx}\], m is a given real number.
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:-
\[\left( x + y \right)\frac{dy}{dx} = 1\]
Find one-parameter families of solution curves of the following differential equation:-
\[x\frac{dy}{dx} + 2y = x^2 \log x\]
Write the differential equation representing family of curves y = mx, where m is arbitrary constant.
The family of curves in which the sub tangent at any point of a curve is double the abscissae, is given by
Find the area of the region bounded by the curves (x -1)2 + y2 = 1 and x2 + y2 = 1, using integration.
The solution of the differential equation `2x * "dy"/"dx" y` = 3 represents a family of ______.
Find the equation of a curve passing through origin and satisfying the differential equation `(1 + x^2) "dy"/"dx" + 2xy` = 4x2
Find the differential equation of system of concentric circles with centre (1, 2).
Find the equation of a curve passing through the point (1, 1). If the tangent drawn at any point P(x, y) on the curve meets the co-ordinate axes at A and B such that P is the mid-point of AB.
The differential equation `y ("d"y)/("d"x) + "c"` represents: ______.
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 ______.
Find the equation of the curve at every point of which the tangent line has a slope of 2x:
The area above the x-axis and under the curve `y = sqrt(1/x - 1)` for `1/2 ≤ x ≤ 1` is:
From the differential equation of the family of circles touching the y-axis at origin
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.
