हिंदी

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

Advertisements
Advertisements

प्रश्न

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

विकल्प

  • `1/x + 1/y` = c

  • logx . logy = c

  • xy = c

  • x + y = c

MCQ
रिक्त स्थान भरें

उत्तर

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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 9: Differential Equations - Solved Examples [पृष्ठ १८८]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
अध्याय 9 Differential Equations
Solved Examples | Q 20 | पृष्ठ १८८

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

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


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

y = ex + 1  :  y″ – y′ = 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


Find the particular solution of the differential equation

`tan x * (dy)/(dx) = 2x tan x + x^2 - y`; `(tan x != 0)` given that y = 0 when `x = pi/2`


The solution of the differential equation \[\frac{dy}{dx} = 1 + x + y^2 + x y^2 , y\left( 0 \right) = 0\] is


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

 

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


cos (x + y) dy = dx


\[\frac{dy}{dx} - y \tan x = - 2 \sin x\]


`(dy)/(dx)+ y tan x = x^n cos x, n ne− 1`


For the following differential equation, find a particular solution satisfying the given condition:

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


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


Solve the following differential equation:-

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


Solve the following differential equation:-

(1 + x2) dy + 2xy dx = cot x dx


Solve the following differential equation:-

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


Solve the following differential equation:-

y dx + (x − y2) dy = 0


Find the general solution of `"dy"/"dx" + "a"y` = emx 


Find the general solution of `(x + 2y^3)  "dy"/"dx"` = y


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


Solve the differential equation dy = cosx(2 – y cosecx) dx given that y = 2 when x = `pi/2`


Solve the differential equation (1 + y2) tan–1xdx + 2y(1 + x2)dy = 0.


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


Find the general solution of `("d"y)/("d"x) -3y = sin2x`


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


Find the general solution of the differential equation:

`(dy)/(dx) = (3e^(2x) + 3e^(4x))/(e^x + e^-x)`


The differential equation of all parabolas that have origin as vertex and y-axis as axis of symmetry is ______.


If the solution curve of the differential equation `(dy)/(dx) = (x + y - 2)/(x - y)` passes through the point (2, 1) and (k + 1, 2), k > 0, then ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×