Advertisements
Advertisements
प्रश्न
Find the differential equation of the family of lines through the origin.
उत्तर
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
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 ellipses having foci on y-axis and centre at origin.
Form the differential equation of the family of hyperbolas having foci on x-axis and centre at 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`
Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.
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 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):
y = eax
Show that y = bex + ce2x is a solution of the differential equation, \[\frac{d^2 y}{d x^2} - 3\frac{dy}{dx} + 2y = 0\]
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:-
\[\left( x \log x \right)\frac{dy}{dx} + y = \log x\]
Find one-parameter families of solution curves of the following differential equation:-
\[\frac{dy}{dx} + y \cos x = e^{\sin x} \cos x\]
Find one-parameter families of solution curves of the following differential equation:-
\[e^{- y} \sec^2 y dy = dx + x dy\]
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.
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 curves y = Ae2x + B.e–2x.
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 differential equation representing the family of curves y = A sinx + B cosx is ______.
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 ______.
The area above the x-axis and under the curve `y = sqrt(1/x - 1)` for `1/2 ≤ x ≤ 1` is:
