हिंदी

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

Advertisements
Advertisements

प्रश्न

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

Advertisements

उत्तर

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
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 hyperbolas having foci on x-axis and centre at origin.


Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.


Form the differential equation of the family of curves represented by y2 = (x − c)3.


Form the differential equation corresponding to y = emx by eliminating m.


Form the differential equation from the following primitive where constants are arbitrary:
y = cx + 2c2 + c3


Form the differential equation corresponding to y2 − 2ay + x2 = a2 by eliminating a.


Form the differential equation of the family of curves represented by the equation (a being the parameter):
 (x − a)2 + 2y2 = a2


Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
x2 − y2 = a2


Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.


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:-

\[\frac{dy}{dx} - \frac{2xy}{1 + x^2} = x^2 + 2\]


Find one-parameter families of solution curves of the following differential equation:-

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


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:-

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


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


The family of curves in which the sub tangent at any point of a curve is double the abscissae, is given by


Find the area of the region bounded by the curves (x -1)2 + y2 = 1 and x2 + y2 = 1, using integration.


Form the differential equation representing the family of curves y = e2x (a + bx), where 'a' and 'b' are arbitrary constants.


Form the differential equation representing the family of curves y = A sin x, by eliminating the arbitrary constant A.


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.


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 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 a curve passing through the point (1, 1). If the tangent drawn at any point P(x, y) on the curve meets the co-ordinate axes at A and B such that P is the mid-point of AB.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×