मराठी

Show that the Family of Curves for Which `Dybydx = (X^2+Y^2)By(2x^2)` is Given by X2 - Y2 = Cx - Mathematics

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प्रश्न

Show that the family of curves for which `dy/dx = (x^2+y^2)/(2x^2)` is given by  x2 - y2 = cx

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उत्तर

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2016-2017 (March) Delhi Set 3

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 representing the family of curves given by (x – a)2 + 2y2 = a2, where a is an arbitrary constant.


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 = cx + 2c2 + c3


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 (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


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(x − a)2 − y2 = 1


Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):

\[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\]

 


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:-

\[\frac{dy}{dx} - y = \cos 2x\]


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:-

\[x \log x\frac{dy}{dx} + y = 2 \log x\]


The differential equation which represents the family of curves y = eCx is


Form the differential equation representing the family of curves y = mx, where m is an arbitrary constant.


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.


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 differential equation representing the family of curves y = A sinx + B cosx is ______.


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)`


The differential equation of the family of curves x2 + y2 – 2ay = 0, where a is arbitrary constant, is ______.


The differential equation representing the family of circles x2 + (y – a)2 = a2 will be of order two.


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:


From the differential equation of the family of circles touching the y-axis at origin


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