Advertisements
Advertisements
प्रश्न
Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.
उत्तर
The equation of the parabola having the vertex at origin and the axis along the positive y-axis is:
`x^2 = 4ay` ......(1)
This is the required differential equation.
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.
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:
y = ax2 + bx + c
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 y2 = a (b − x2) by eliminating a and b.
Form the differential equation corresponding to y2 − 2ay + x2 = a2 by eliminating a.
Form the differential equation corresponding to (x − a)2 + (y − b)2 = r2 by eliminating a and b.
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):
(x − a)2 − y2 = 1
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
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 the equation of a curve passing through the point (0, 0) and whose differential equation is \[\frac{dy}{dx} = e^x \sin x\]
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:-
\[x\frac{dy}{dx} + y = x^4\]
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:-
\[\frac{dy}{dx} - \frac{2xy}{1 + x^2} = x^2 + 2\]
Find one-parameter families of solution curves of the following differential equation:-
\[x \log x\frac{dy}{dx} + y = 2 \log x\]
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.
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 ______.
Form the differential equation of all circles which pass through origin and whose centres lie on y-axis.
Form the differential equation by eliminating A and B in Ax2 + By2 = 1
Find the equation of a curve passing through (2, 1) if the slope of the tangent to the curve at any point (x, y) is `(x^2 + y^2)/(2xy)`.
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 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.
The differential equation `y ("d"y)/("d"x) + "c"` represents: ______.
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