English

Find the Differential Equation of the Family of Concentric Circles `X^2 + Y^2 = A^2` - Mathematics

Advertisements
Advertisements

Question

Find the differential equation of the family of concentric circles `x^2 + y^2 = a^2`

Solution

Finally of concentric circle is `x^2 + y^2 = a^2`

∴DDifferential w.r.t x

`2x + 2y dy/dx = 0`

`:. y dy/dx + x = 0`

shaalaa.com
  Is there an error in this question or solution?
2017-2018 (March) Set 1

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

If   `y=sqrt(sinx+sqrt(sinx+sqrt(sinx+..... oo))),` then show that `dy/dx=cosx/(2y-1)`


The solution of the differential equation dy/dx = sec x – y tan x is:

(A) y sec x = tan x + c

(B) y sec x + tan x = c

(C) sec x = y tan x + c

(D) sec x + y tan x = c


Find the particular solution of the differential equation  `e^xsqrt(1-y^2)dx+y/xdy=0` , given that y=1 when x=0


Find the particular solution of differential equation:

`dy/dx=-(x+ycosx)/(1+sinx) " given that " y= 1 " when "x = 0`


Find the particular solution of the differential equation x (1 + y2) dx – y (1 + x2) dy = 0, given that y = 1 when x = 0.


Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:

y = x2 + 2x + C  :  y′ – 2x – 2 = 0


Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:

`y sqrt(1 + x^2) : y' = (xy)/(1+x^2)`


Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:

y = x sin x : xy' = `y + x  sqrt (x^2 - y^2)`  (x ≠ 0 and x > y or x < -y)


How many arbitrary constants are there in the general solution of the differential equation of order 3.


The general solution of the differential equation \[\frac{dy}{dx} + y\] g' (x) = g (x) g' (x), where g (x) is a given function of x, is


The solution of the differential equation \[2x\frac{dy}{dx} - y = 3\] represents


Write the solution of the differential equation \[\frac{dy}{dx} = 2^{- y}\] .


Solve the differential equation (x2 − yx2) dy + (y2 + x2y2) dx = 0, given that y = 1, when x = 1.


x (e2y − 1) dy + (x2 − 1) ey dx = 0


\[\frac{dy}{dx} + 1 = e^{x + y}\]


For the following differential equation, find the general solution:- \[\frac{dy}{dx} = \sqrt{4 - y^2}, - 2 < y < 2\]


For the following differential equation, find a particular solution satisfying the given condition:- \[\cos\left( \frac{dy}{dx} \right) = a, y = 1\text{ when }x = 0\]


For the following differential equation, find a particular solution satisfying the given condition:- \[\frac{dy}{dx} = y \tan x, y = 1\text{ when }x = 0\]


Solve the following differential equation:- \[\left( x - y \right)\frac{dy}{dx} = x + 2y\]


Solve the following differential equation:- \[x \cos\left( \frac{y}{x} \right)\frac{dy}{dx} = y \cos\left( \frac{y}{x} \right) + x\]


Solve the following differential equation:-

\[\left( x + y \right)\frac{dy}{dx} = 1\]


Find the equation of a curve passing through the point (0, 0) and whose differential equation is \[\frac{dy}{dx} = e^x \sin x.\]


Solve the differential equation : `("x"^2 + 3"xy" + "y"^2)d"x" - "x"^2 d"y" = 0  "given that"  "y" = 0  "when"  "x" = 1`.


Form the differential equation having y = (sin–1x)2 + Acos–1x + B, where A and B are arbitrary constants, as its general solution.


The solution of the differential equation `("d"y)/("d"x) + (1 + y^2)/(1 + x^2)` is ______.


General solution of `("d"y)/("d"x) + ytanx = secx` is ______.


Number of arbitrary constants in the particular solution of a differential equation of order two is two.


Find a particular solution satisfying the given condition `- cos((dy)/(dx)) = a, (a ∈ R), y` = 1 when `x` = 0


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×