हिंदी

How Many Arbitrary Constants Are There in the General Solution of the Differential Equation of Order 3.

Advertisements
Advertisements

प्रश्न

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

Advertisements

उत्तर

The arbitrary constants in the general solution of the differential equation is equal to the order of the differential equation.
Hence, the number of arbitrary constants in the general solution of the differential equation of order 3 are 3.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 21: Differential Equations - Very Short Answers [पृष्ठ १३९]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 21 Differential Equations
Very Short Answers | Q 27 | पृष्ठ १३९

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Solve : 3ex tanydx + (1 +ex) sec2 ydy = 0

Also, find the particular solution when x = 0 and y = π.


Solve the differential equation `dy/dx=(y+sqrt(x^2+y^2))/x`


Find the particular solution of the differential equation

(1 – y2) (1 + log x) dx + 2xy dy = 0, given that y = 0 when x = 1.


Find the general solution of the following differential equation : 

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


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


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

`y = sqrt(a^2 - x^2 )  x in (-a,a) : x + y  dy/dx = 0(y != 0)`


Find a particular solution of the differential equation `dy/dx + y cot x = 4xcosec x(x != 0)`, given that y = 0 when `x = pi/2.`


Find `(dy)/(dx)` at x = 1, y = `pi/4` if `sin^2 y + cos xy = K`


The population of a town grows at the rate of 10% per year. Using differential equation, find how long will it take for the population to grow 4 times.


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


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


\[\frac{dy}{dx} = \frac{\sin x + x \cos x}{y\left( 2 \log y + 1 \right)}\]


\[\frac{dy}{dx} - y \cot x = cosec\ x\]


\[\frac{dy}{dx} - y \tan x = e^x \sec x\]


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


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 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:- `y dx + x log  (y)/(x)dy-2x dy=0`


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:-

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


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.`


Find the differential equation of all non-horizontal lines in a plane.


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


Solution of differential equation xdy – ydx = 0 represents : ______.


Integrating factor of the differential equation `cosx ("d"y)/("d"x) + ysinx` = 1 is ______.


Solution of `("d"y)/("d"x) - y` = 1, y(0) = 1 is given by ______.


Integrating factor of the differential equation `("d"y)/("d"x) + y tanx - secx` = 0 is ______.


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


The integrating factor of the differential equation `("d"y)/("d"x) + y = (1 + y)/x` is ______.


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


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


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


The solution of the differential equation `("d"y)/("d"x) = (x + 2y)/x` is x + y = kx2.


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 general solution of the differential equation:

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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×