English

The number of arbitrary constants in the particular solution of a differential equation of third order are ______.

Advertisements
Advertisements

Question

The number of arbitrary constants in the particular solution of a differential equation of third order are ______.

Options

  • 3

  • 2

  • 1

  • 0

MCQ
Fill in the Blanks
Advertisements

Solution

The number of arbitrary constants in the particular solution of a differential equation of third order are 0.

Explanation:

In the particular solution of a third-order differential equation, there is no arbitrary constant.

shaalaa.com
  Is there an error in this question or solution?
Chapter 9: Differential Equations - Exercise 9.2 [Page 385]

APPEARS IN

NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 9 Differential Equations
Exercise 9.2 | Q 12 | Page 385

RELATED QUESTIONS

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`


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


If x = Φ(t) differentiable function of ‘ t ' then prove that `int f(x) dx=intf[phi(t)]phi'(t)dt`


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.


If y = P eax + Q ebx, show that

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


Solve the differential equation `dy/dx -y =e^x`


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)`


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

x + y = tan–1y   :   y2 y′ + y2 + 1 = 0


Solve the differential equation `cos^2 x dy/dx` + y = tan x


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


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


The general solution of the differential equation \[\frac{dy}{dx} + y \] cot x = cosec x, is


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


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


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


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


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


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:- \[\frac{dy}{dx} = \frac{1 - \cos x}{1 + \cos x}\]


Solve the following differential equation:-

\[x\frac{dy}{dx} + 2y = x^2 , x \neq 0\]


Solve the following differential equation:-

y dx + (x − y2) dy = 0


Find the equation of the curve passing through the point (1, 1) whose differential equation is x dy = (2x2 + 1) dx, x ≠ 0.


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


The general solution of the differential equation `"dy"/"dx" + y/x` = 1 is ______.


The general solution of the differential equation `"dy"/"dx" + y sec x` = tan x is y(secx – tanx) = secx – tanx + x + k.


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


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


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


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


General solution of the differential equation of the type `("d"x)/("d"x) + "P"_1x = "Q"_1` is given by ______.


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:

`log((dy)/(dx)) = ax + by`.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×