English

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

Advertisements
Advertisements

Question

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

Options

  • True

  • False

MCQ
True or False
Advertisements

Solution

This statement is False.

Explanation:

Since particular solution of a differential equation has no arbitrary constant.

shaalaa.com
  Is there an error in this question or solution?
Chapter 9: Differential Equations - Exercise [Page 203]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 12
Chapter 9 Differential Equations
Exercise | Q 77.(v) | Page 203

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`


Solve the differential equation:  `x+ydy/dx=sec(x^2+y^2)` Also find the particular solution if x = y = 0.


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`


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


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 particular solution of the differential equation dy/dx=1 + x + y + xy, given that y = 0 when x = 1.


Find the particular solution of the differential equation log(dy/dx)= 3x + 4y, given that y = 0 when x = 0.


The number of arbitrary constants in the general solution of a differential equation of fourth order are ______.


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


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


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


The solution of the differential equation \[\frac{dy}{dx} = \frac{y}{x} + \frac{\phi\left( \frac{y}{x} \right)}{\phi'\left( \frac{y}{x} \right)}\] is


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


cos (x + y) dy = dx


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


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


(1 + y + x2 y) dx + (x + x3) dy = 0


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


\[\frac{dy}{dx} + 2y = \sin 3x\]


\[\frac{dy}{dx} + y = 4x\]


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


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:- \[\frac{dy}{dx} = y \tan x, y = 1\text{ when }x = 0\]


Solve the following differential equation:-

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


Solve the following differential equation:-

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


Solve the following differential equation:-

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


Solve the following differential equation:-

y dx + (x − y2) dy = 0


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


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


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


The general solution of `("d"y)/("d"x) = 2x"e"^(x^2 - y)` is ______.


General solution of `("d"y)/("d"x) + ytanx = secx` is ______.


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


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 ______.


The member of arbitrary constants in the particulars solution of a differential equation of third order as


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 ______.


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×