English

Solution of the differential equation dxdydxx+dyy = 0 is ______. - Mathematics

Advertisements
Advertisements

Question

Solution of the differential equation `"dx"/x + "dy"/y` = 0 is ______.

Options

  • `1/x + 1/y` = c

  • logx . logy = c

  • xy = c

  • x + y = c

MCQ
Fill in the Blanks

Solution

Solution of the differential equation `"dx"/x + "dy"/y` = 0 is xy = c.

Explanation:

From the given equation,

We get logx + logy = logc giving xy = c.

shaalaa.com
  Is there an error in this question or solution?
Chapter 9: Differential Equations - Solved Examples [Page 188]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 12
Chapter 9 Differential Equations
Solved Examples | Q 20 | Page 188

RELATED QUESTIONS

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


The differential equation of the family of curves y=c1ex+c2e-x is......

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

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

(c)`(d^2y)/dx^2+1=0`

(d)`(d^2y)/dx^2-1=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:

xy = log y + C :  `y' = (y^2)/(1 - xy) (xy != 1)`


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 solution of the differential equation (x2 + 1) \[\frac{dy}{dx}\] + (y2 + 1) = 0, is


x (e2y − 1) dy + (x2 − 1) ey dx = 0


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


(x + y − 1) dy = (x + y) dx


`(2ax+x^2)(dy)/(dx)=a^2+2ax`


Find the general solution of the differential equation \[\frac{dy}{dx} = \frac{x + 1}{2 - y}, y \neq 2\]


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:-

(1 + x2) dy + 2xy dx = cot x dx


Find a particular solution of the following differential equation:- x2 dy + (xy + y2) dx = 0; y = 1 when x = 1


Find the equation of a curve passing through the point (−2, 3), given that the slope of the tangent to the curve at any point (xy) is `(2x)/y^2.`


Solve the differential equation:  ` ("x" + 1) (d"y")/(d"x") = 2e^-"y" - 1; y(0) = 0.`


The number of arbitrary constants in a particular solution of the differential equation tan x dx + tan y dy = 0 is ______.


y = x is a particular solution of the differential equation `("d"^2y)/("d"x^2) - x^2 "dy"/"dx" + xy` = x.


Integrating factor of `(x"d"y)/("d"x) - y = x^4 - 3x` is ______.


The solution of `x ("d"y)/("d"x) + y` = ex is ______.


The general solution of the differential equation (ex + 1) ydy = (y + 1) exdx is ______.


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


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


Polio drops are delivered to 50 K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation `"dy"/"dx" = "k"(50 - "y")` where x denotes the number of weeks and y the number of children who have been given the drops.

The value of c in the particular solution given that y(0) = 0 and k = 0.049 is ______.


Find the particular solution of the following differential equation, given that y = 0 when x = `pi/4`.

`(dy)/(dx) + ycotx = 2/(1 + sinx)`


Find the particular solution of the differential equation `x (dy)/(dx) - y = x^2.e^x`, given y(1) = 0.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×