Advertisements
Advertisements
प्रश्न
Family y = Ax + A3 of curves is represented by the differential equation of degree ______.
विकल्प
1
2
3
4
उत्तर
Family y = Ax + A3 of curves is represented by the differential equation of degree 1.
Explanation:
Given equation is y = Ax + A3
Differentiating both sides, we get
`("d"y)/("d"x)` = A which has degree 1.
APPEARS IN
संबंधित प्रश्न
Form the differential equation of the family of hyperbolas having foci on x-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`
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
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):
y2 = 4a (x − b)
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 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:-
\[x\frac{dy}{dx} - y = \left( x + 1 \right) e^{- x}\]
Find one-parameter families of solution curves of the following differential equation:-
\[\left( x \log x \right)\frac{dy}{dx} + y = \log x\]
Write the order of the differential equation representing the family of curves y = ax + a3.
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 = 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 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)`
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 ______.
Family y = Ax + A3 of curves will correspond to a differential equation of order ______.
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 ______.
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.
Form the differential equation of family of circles having centre on y-axis and raduis 3 units
