Advertisements
Advertisements
प्रश्न
Form the differential equation representing the family of curves y = mx, where m is an arbitrary constant.
उत्तर
We have,
y = mx .........(1)
Differentiating both sides, we get
\[\frac{dy}{dx} = m\]
\[ \Rightarrow \frac{dy}{dx} = \frac{y}{x} ............\left[\text{From (1)} \right]\]
\[ \Rightarrow x\frac{dy}{dx} = y\]
\[ \Rightarrow x\frac{dy}{dx} - y = 0\]
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 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 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 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
Show that the family of curves for which `dy/dx = (x^2+y^2)/(2x^2)` is given by x2 - y2 = cx
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
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
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):
y2 = 4a (x − b)
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:-
\[e^{- y} \sec^2 y dy = dx + x dy\]
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.
Form the differential equation representing the family of curves y = A sin x, by eliminating the arbitrary constant A.
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
Family y = Ax + A3 of curves is represented by the differential equation of degree ______.
The differential equation `y ("d"y)/("d"x) + "c"` represents: ______.
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 ______.
The differential equation representing the family of circles x2 + (y – a)2 = a2 will be of order two.
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:
