Advertisements
Advertisements
प्रश्न
Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.
Advertisements
उत्तर
The equation of the parabola having the vertex at origin and the axis along the positive y-axis is:
`x^2 = 4ay` ......(1)
This is the required differential equation.
APPEARS IN
संबंधित प्रश्न
Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.
Form the differential equation from the following primitive where constants are arbitrary:
xy = a2
Find the differential equation of the family of curves y = Ae2x + Be−2x, where A and B are arbitrary constants.
Form the differential equation corresponding to (x − a)2 + (y − b)2 = r2 by eliminating a and b.
Form the differential equation of the family of curves represented by the equation (a being the parameter):
(2x − a)2 − y2 = a2
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 = ax3
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:-
\[\frac{dy}{dx} + 3y = e^{mx}\], m is a given real number.
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:-
\[x\frac{dy}{dx} - y = \left( x + 1 \right) e^{- x}\]
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:-
\[\left( x \log x \right)\frac{dy}{dx} + y = \log x\]
Find one-parameter families of solution curves of the following differential equation:-
\[\left( x + y \right)\frac{dy}{dx} = 1\]
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 of the family of hyperbolas having foci on x-axis and centre at the origin.
Form the differential equation representing the family of curves `y2 = m(a2 - x2) by eliminating the arbitrary constants 'm' and 'a'.
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.
The solution of the differential equation `2x * "dy"/"dx" y` = 3 represents a family of ______.
The differential equation representing the family of curves y = A sinx + B cosx is ______.
Form the differential equation of all circles which pass through origin and whose centres lie on y-axis.
Find the equation of a curve passing through origin and satisfying the differential equation `(1 + x^2) "dy"/"dx" + 2xy` = 4x2
Form the differential equation by eliminating A and B in Ax2 + By2 = 1
Find the equation of a curve passing through (2, 1) if the slope of the tangent to the curve at any point (x, y) is `(x^2 + y^2)/(2xy)`.
Find the equation of the curve through the point (1, 0) if the slope of the tangent to the curve at any point (x, y) is `(y - 1)/(x^2 + x)`
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 of the family of curves x2 + y2 – 2ay = 0, where a is arbitrary constant, is ______.
The differential equation of the family of curves y2 = 4a(x + a) is ______.
From the differential equation of the family of circles touching the y-axis at origin
