Advertisements
Advertisements
प्रश्न
Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.
उत्तर
The equation of a circle in the first quadrant with centre (a, a) and radius (a) which touches the coordinate axes is:
APPEARS IN
संबंधित प्रश्न
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 ellipses having foci on y-axis and centre at origin.
Form the differential equation of the family of circles having centre on y-axis and radius 3 units.
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`
Form the differential equation from the following primitive where constants are arbitrary:
y2 = 4ax
Form the differential equation from the following primitive where constants are arbitrary:
y = cx + 2c2 + c3
Form the differential equation of the family of curves represented by the equation (a being the parameter):
(2x + a)2 + y2 = a2
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):
x2 + y2 = 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):
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):
x2 + y2 = 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:-
\[x\frac{dy}{dx} - y = \left( x + 1 \right) e^{- x}\]
Write the order of the differential equation representing the family of curves y = ax + a3.
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 = mx, where m is an arbitrary constant.
Form the differential equation of the family of ellipses having foci on y-axis and centre at the origin.
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.
Find the differential equation of the family of lines through the origin.
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 by eliminating A and B in Ax2 + By2 = 1
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.
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.
Family y = Ax + A3 of curves is represented by the differential equation of degree ______.
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 ______.
Differential equation representing the family of curves y = ex (Acosx + Bsinx) is `("d"^2y)/("d"x^2) - 2 ("d"y)/("d"x) + 2y` = 0
The area above the x-axis and under the curve `y = sqrt(1/x - 1)` for `1/2 ≤ x ≤ 1` is:
Form the differential equation of family of circles having centre on y-axis and raduis 3 units
