Advertisements
Advertisements
प्रश्न
Family y = Ax + A3 of curves will correspond to a differential equation of order ______.
पर्याय
3
2
1
Not defined
उत्तर
Family y = Ax + A3 of curves will correspond to a differential equation of order 2.
Explanation:
The given equation is y = Ax + A3
Differentiating both sides, we get `("d"y)/("d"x)` = A
Again differentiating both sides,
We have `("d"^2y)/("d"x^2)` = 0
So the order of the differential equation is 2.
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`
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:
y2 = 4ax
Form the differential equation from the following primitive where constants are arbitrary:
xy = 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):
(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
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
y = eax
Find one-parameter families of solution curves of the following differential equation:-
\[\frac{dy}{dx} + 3y = e^{mx}\], m is a given real number.
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:-
\[x\frac{dy}{dx} + y = x^4\]
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:-
\[\frac{dy}{dx} \cos^2 x = \tan x - y\]
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
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.
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 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 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.
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