English

The Number of Arbitrary Constants in the General Solution of Differential Equation of Fourth Order is - Mathematics

Advertisements
Advertisements

Question

The number of arbitrary constants in the general solution of differential equation of fourth order is

Options

  • 0

  • 2

  • 3

  • 4

MCQ

Solution

4

 

The number of arbitrary constants in the general solution of a differential equation of order n is n.

Thus, the number of arbitrary constants in the general solution of differential equation of fourth order is 4.

shaalaa.com
  Is there an error in this question or solution?
Chapter 22: Differential Equations - MCQ [Page 143]

APPEARS IN

RD Sharma Mathematics [English] Class 12
Chapter 22 Differential Equations
MCQ | Q 43 | Page 143

RELATED QUESTIONS

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

y = x2 + 2x + C  :  y′ – 2x – 2 = 0


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


Solve the differential equation `[e^(-2sqrtx)/sqrtx - y/sqrtx] dx/dy = 1 (x != 0).`


if `y = sin^(-1) (6xsqrt(1-9x^2))`, `1/(3sqrt2) < x < 1/(3sqrt2)` then find `(dy)/(dx)`


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`


Solve the differential equation:

`e^(x/y)(1-x/y) + (1 + e^(x/y)) dx/dy = 0` when x = 0, y = 1


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


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


Solution of the differential equation \[\frac{dy}{dx} + \frac{y}{x}=\sin x\] is


The solution of the differential equation \[\frac{dy}{dx} + 1 = e^{x + y}\], is


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


Solve the differential equation (x2 − yx2) dy + (y2 + x2y2) dx = 0, given that y = 1, when x = 1.


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


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


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


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


\[\frac{dy}{dx} + 5y = \cos 4x\]


`x cos x(dy)/(dx)+y(x sin x + cos x)=1`


For the following differential equation, find the general solution:- \[\frac{dy}{dx} = \frac{1 - \cos x}{1 + \cos x}\]


For the following differential equation, find the general solution:- \[\frac{dy}{dx} + y = 1\]


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:-

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


Solve the following differential equation:-

\[\frac{dy}{dx} + 3y = e^{- 2x}\]


Solve the following differential equation:-

y dx + (x − y2) dy = 0


Solve the following differential equation:-

\[\left( x + 3 y^2 \right)\frac{dy}{dx} = y\]


Find a particular solution of the following differential equation:- \[\left( 1 + x^2 \right)\frac{dy}{dx} + 2xy = \frac{1}{1 + x^2}; y = 0,\text{ when }x = 1\]


The solution of the differential equation `x "dt"/"dx" + 2y` = x2 is ______.


The general solution of the differential equation x(1 + y2)dx + y(1 + x2)dy = 0 is (1 + x2)(1 + y2) = k.


x + y = tan–1y is a solution of the differential equation `y^2 "dy"/"dx" + y^2 + 1` = 0.


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


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


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 the differential equation (ex + 1) ydy = (y + 1) exdx is ______.


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×