हिंदी

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

Advertisements
Advertisements

प्रश्न

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

उत्तर

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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
2017-2018 (March) Set 1

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

The differential equation of `y=c/x+c^2` is :

(a)`x^4(dy/dx)^2-xdy/dx=y`

(b)`(d^2y)/dx^2+xdy/dx+y=0`

(c)`x^3(dy/dx)^2+xdy/dx=y`

(d)`(d^2y)/dx^2+dy/dx-y=0`


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


Find the general solution of the following differential equation : 

`(1+y^2)+(x-e^(tan^(-1)y))dy/dx= 0`


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

y – cos y = x :  (y sin y + cos y + x) y′ = y


if `y = sin^(-1) (6xsqrt(1-9x^2))`, `1/(3sqrt2) < x < 1/(3sqrt2)` then find `(dy)/(dx)`


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 \[\frac{dy}{dx} = 1 + x + y^2 + x y^2 , y\left( 0 \right) = 0\] is


If m and n are the order and degree of the differential equation \[\left( y_2 \right)^5 + \frac{4 \left( y_2 \right)^3}{y_3} + y_3 = x^2 - 1\], then


The number of arbitrary constants in the general solution of differential equation of fourth order is


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


(x3 − 2y3) dx + 3x2 y dy = 0


`x cos x(dy)/(dx)+y(x sin x + cos x)=1`


Find the particular solution of the differential equation \[\frac{dy}{dx} = - 4x y^2\] given that y = 1, when x = 0.


For the following differential equation, find the general solution:- `y log y dx − x dy = 0`


For the following differential equation, find the general solution:- \[\frac{dy}{dx} = \sin^{- 1} x\]


Solve the following differential equation:-

\[\frac{dy}{dx} + 3y = e^{- 2x}\]


Solve the following differential equation:-

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


Solve the following differential equation:-

\[\left( x + 3 y^2 \right)\frac{dy}{dx} = y\]


Solve the differential equation: `(d"y")/(d"x") - (2"x")/(1+"x"^2) "y" = "x"^2 + 2`


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


If y(x) is a solution of `((2 + sinx)/(1 + y))"dy"/"dx"` = – cosx and y (0) = 1, then find the value of `y(pi/2)`.


Solve: `y + "d"/("d"x) (xy) = x(sinx + logx)`


tan–1x + tan–1y = c is the general solution of the differential equation ______.


The solution of the differential equation cosx siny dx + sinx cosy dy = 0 is ______.


The solution of the equation (2y – 1)dx – (2x + 3)dy = 0 is ______.


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


The solution of the differential equation ydx + (x + xy)dy = 0 is ______.


The solution of `("d"y)/("d"x) = (y/x)^(1/3)` is `y^(2/3) - x^(2/3)` = c.


Solve the differential equation:

`(xdy - ydx)  ysin(y/x) = (ydx + xdy)  xcos(y/x)`.

Find the particular solution satisfying the condition that y = π when x = 1.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×