English

Form a Differential Equation Representing the Given Family of Curves by Eliminating Arbitrary Constants a and B. X/A + Y/B = 1 - Mathematics

Advertisements
Advertisements

Question

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.

`x/a + y/b = 1`

Solution

`x/a + y/b = 1`

Differentiating both sides of the given equation with respect to x, we get:

Hence, the required differential equation of the given curve is y" = 0

shaalaa.com
  Is there an error in this question or solution?
Chapter 9: Differential Equations - Exercise 9.3 [Page 391]

APPEARS IN

NCERT Mathematics [English] Class 12
Chapter 9 Differential Equations
Exercise 9.3 | Q 1 | Page 391

RELATED QUESTIONS

Find the differential equation representing the family of curves v=A/r+ B, where A and B are arbitrary constants.


Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.

y2 = a (b2 – x2)


Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.

y = a e3x + b e– 2x


Find the particular solution of the differential equation (1 + e2x) dy + (1 + y2) ex dx = 0, given that y = 1 when x = 0.


Solve the differential equation  `ye^(x/y) dx = (xe^(x/y) + y^2)dy, (y != 0)`


Find a particular solution of the differential equation (x - y) (dx + dy) = dx - dy, given that y = -1, when x = 0. (Hint: put x - y = t)


The general solution of the differential equation `(y dx - x dy)/y = 0` is ______.


The general solution of a differential equation of the type  `dx/dy + P_1 x = Q_1` is ______.


The general solution of the differential equation ex dy + (y ex + 2x) dx = 0 is ______.


Find the differential equation of all the circles which pass through the origin and whose centres lie on y-axis.


The equation of the curve satisfying the differential equation y (x + y3) dx = x (y3 − x) dy and passing through the point (1, 1) is


Verify that xy = a ex + b ex + x2 is a solution of the differential equation \[x\frac{d^2 y}{d x^2} + 2\frac{dy}{dx} - xy + x^2 - 2 = 0.\]


Show that y = C x + 2C2 is a solution of the differential equation \[2 \left( \frac{dy}{dx} \right)^2 + x\frac{dy}{dx} - y = 0.\]


Show that y2 − x2 − xy = a is a solution of the differential equation \[\left( x - 2y \right)\frac{dy}{dx} + 2x + y = 0.\]


Verify that y = A cos x + sin x satisfies the differential equation \[\cos x\frac{dy}{dx} + \left( \sin x \right)y=1.\]


Find the differential equation corresponding to y = ae2x + be3x + cex where abc are arbitrary constants.


From x2 + y2 + 2ax + 2by + c = 0, derive a differential equation not containing a, b and c.


\[\frac{dy}{dx} = \sin^3 x \cos^4 x + x\sqrt{x + 1}\]


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


\[\frac{dy}{dx} - x \sin^2 x = \frac{1}{x \log x}\]


\[\frac{dy}{dx} = \sin^3 x \cos^2 x + x e^x\]


(1 + xy dx + (1 + yx dy = 0


cos y log (sec x + tan x) dx = cos x log (sec y + tan y) dy


Solve the differential equation:

cosec3 x dy − cosec y dx = 0


The general solution of the differential equation `(dy)/(dx) + x/y` = 0 is


If n is any integer, then the general solution of the equation `cos x - sin x = 1/sqrt(2)` is


General solution of tan 5θ = cot 2θ is


The general solution of the differential equation `x^xdy + (ye^x + 2x)  dx` = 0


Find the general solution of differential equation `(dy)/(dx) = (1 - cosx)/(1 + cosx)`


What is the general solution of differential equation `(dy)/(dx) = sqrt(4 - y^2)  (-2 < y < 2)`


Solve the differential equation: y dx + (x – y2)dy = 0


The general solution of the differential equation ydx – xdy = 0; (Given x, y > 0), is of the form

(Where 'c' is an arbitrary positive constant of integration)


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×