मराठी

Find the differential equation of the family of lines through the origin. - Mathematics

Advertisements
Advertisements

प्रश्न

Find the differential equation of the family of lines through the origin.

बेरीज
Advertisements

उत्तर

Let y = mx be the family of lines through origin.

Therefore, `"dy"/"dx"` = m

Eliminating m,

We get y = `"dy"/"dx" * x` or `x "dy"/"dx" - y` = 0.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 9: Differential Equations - Solved Examples [पृष्ठ १८२]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
पाठ 9 Differential Equations
Solved Examples | Q 5 | पृष्ठ १८२

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`

 

 

 


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


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:
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 y2 − 2ay + x2 = a2 by eliminating a.


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):

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

 


Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
y2 = 4a (x − b)

 


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


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 order of the differential equation representing the family of curves y = ax + a3.


Form the differential equation of the family of ellipses having foci on y-axis and centre at the origin.


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


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 solution of the differential equation `2x * "dy"/"dx" y` = 3 represents a family of ______.


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 


Form the differential equation by eliminating A and B in Ax2 + By2 = 1


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)`


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.


Family y = Ax + A3 of curves is represented by the differential equation of degree ______.


Family y = Ax + A3 of curves will correspond to a differential equation of order ______.


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.


Differential equation representing the family of curves y = ex (Acosx + Bsinx) is `("d"^2y)/("d"x^2) - 2 ("d"y)/("d"x) + 2y` = 0


Find the equation of the curve at every point of which the tangent line has a slope of 2x:


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


Form the differential equation of the family of hyperbola having foci on x-axis and centre at origin.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×