Advertisements
Advertisements
प्रश्न
The differential equation representing the family of circles x2 + (y – a)2 = a2 will be of order two.
विकल्प
True
False
Advertisements
उत्तर
This statement is False.
Explanation:
We know that the order of the differential equation is equal to the number of arbitrary constants.
APPEARS IN
संबंधित प्रश्न
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`
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
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 = ax2 + bx + c
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 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
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
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):
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 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:-
\[\frac{dy}{dx} + y \cos x = e^{\sin x} \cos x\]
Write the differential equation representing family of curves y = mx, where m is arbitrary constant.
The differential equation which represents the family of curves y = eCx is
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 representing the family of curves y = e2x (a + bx), where 'a' and 'b' are arbitrary constants.
Find the equation of a curve whose tangent at any point on it, different from origin, has slope `y + y/x`.
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.
Find the equation of a curve passing through origin and satisfying the differential equation `(1 + x^2) "dy"/"dx" + 2xy` = 4x2
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: ______.
The differential equation of the family of curves x2 + y2 – 2ay = 0, where a is arbitrary constant, is ______.
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 ______.
Differential equation representing the family of curves y = ex (Acosx + Bsinx) is `("d"^2y)/("d"x^2) - 2 ("d"y)/("d"x) + 2y` = 0
Form the differential equation of the family of hyperbola having foci on x-axis and centre at origin.
