Advertisements
Advertisements
प्रश्न
Write the differential equation representing family of curves y = mx, where m is arbitrary constant.
Advertisements
उत्तर
We have,
\[y = mx . . . . . \left( 1 \right) \]
Differentiating with respect to x
\[ \Rightarrow \frac{dy}{dx} = m\]
\[\text{ Substituting the value of m }= \frac{dy}{dx} \text{ in eq }\left( 1 \right)\text{ we get , }\]
\[y = x\frac{dy}{dx}\]
\[\text{ Hence, }y = x\frac{dy}{dx} \text{ is the required differential equation . }\]
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 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 representing the family of curves given by (x – a)2 + 2y2 = a2, where a is an arbitrary constant.
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 from the following primitive where constants are arbitrary:
xy = a2
Find the differential equation of the family of curves, x = A cos nt + B sin nt, where A and B are arbitrary constants.
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):
x2 + (y − b)2 = 1
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
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:-
\[\left( x + y \right)\frac{dy}{dx} = 1\]
Find one-parameter families of solution curves of the following differential equation:-
\[e^{- y} \sec^2 y dy = dx + x dy\]
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.
Form the differential equation of the family of ellipses having foci on y-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 = e2x (a + bx), where 'a' and 'b' are arbitrary constants.
Form the differential equation representing the family of curves y = A sin x, by eliminating the arbitrary constant A.
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 ______.
Form the differential equation by eliminating A and B in Ax2 + By2 = 1
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 `y ("d"y)/("d"x) + "c"` represents: ______.
Find the equation of the curve at every point of which the tangent line has a slope of 2x:
From the differential equation of the family of circles touching the y-axis at origin
Form the differential equation of family of circles having centre on y-axis and raduis 3 units
