Advertisements
Advertisements
प्रश्न
Form the differential equation representing the family of curves y = A sin x, by eliminating the arbitrary constant A.
Advertisements
उत्तर
Given y = A sin x ..........(1)
Differentiating with respect to x
`"dy"/"dx" = "A"cos"x"` ......(2)
From (1) and (2) we have
`"dy"/"dx" = "y"/sin"x" . cos"x"`
⇒ `"dy"/"dx" - (cot"x")"y" = 0`
APPEARS IN
संबंधित प्रश्न
Form the differential equation of the family of circles having centre on y-axis and radius 3 units.
Which of the following differential equations has y = c1 ex + c2 e–x as the general solution?
(A) `(d^2y)/(dx^2) + y = 0`
(B) `(d^2y)/(dx^2) - y = 0`
(C) `(d^2y)/(dx^2) + 1 = 0`
(D) `(d^2y)/(dx^2) - 1 = 0`
Form the differential equation representing the family of curves given by (x – a)2 + 2y2 = a2, where a is an arbitrary constant.
Form the differential equation corresponding to y = emx by eliminating m.
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):
x2 − y2 = a2
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
x2 + (y − b)2 = 1
Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.
For the differential equation xy \[\frac{dy}{dx}\] = (x + 2) (y + 2). Find the solution curve passing through the point (1, −1).
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:-
\[\frac{dy}{dx} \cos^2 x = \tan x - y\]
Find one-parameter families of solution curves of the following differential equation:-
\[x \log x\frac{dy}{dx} + y = 2 \log x\]
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
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.
Find the differential equation of the family of curves y = Ae2x + B.e–2x.
Find the differential equation of the family of lines through the origin.
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 ______.
The differential equation `y ("d"y)/("d"x) + "c"` represents: ______.
Family y = Ax + A3 of curves will correspond to a differential equation of order ______.
Differential equation representing the family of curves y = ex (Acosx + Bsinx) is `("d"^2y)/("d"x^2) - 2 ("d"y)/("d"x) + 2y` = 0
