मराठी

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

Advertisements
Advertisements

प्रश्न

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

पर्याय

  • 0

  • 2

  • 3

  • 4

MCQ
रिकाम्या जागा भरा
Advertisements

उत्तर

The number of arbitrary constants in the general solution of a differential equation of fourth order are 4.

Explanation: 

The generic solution of an nth order differential equation has n arbitrary constants.

So the fourth-order differential equation contains four constants.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 9: Differential Equations - Exercise 9.2 [पृष्ठ ३८५]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
पाठ 9 Differential Equations
Exercise 9.2 | Q 11 | पृष्ठ ३८५

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

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 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 = x sin x : xy' = `y + x  sqrt (x^2 - y^2)`  (x ≠ 0 and x > y or x < -y)


Show that the general solution of the differential equation  `dy/dx + (y^2 + y +1)/(x^2 + x + 1) = 0` is given by (x + y + 1) = A (1 - x - y - 2xy), where A is parameter.


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.`


If y = etan x+ (log x)tan x 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`


The solution of the differential equation \[\frac{dy}{dx} + \frac{2y}{x} = 0\] with y(1) = 1 is given by


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


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


The general solution of a differential equation of the type \[\frac{dx}{dy} + P_1 x = Q_1\] is


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


(1 + y + x2 y) dx + (x + x3) dy = 0


`2 cos x(dy)/(dx)+4y sin x = sin 2x," given that "y = 0" when "x = pi/3.`


Solve the differential equation:

(1 + y2) dx = (tan1 y x) dy


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

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


Solve the following differential equation:- \[x \cos\left( \frac{y}{x} \right)\frac{dy}{dx} = y \cos\left( \frac{y}{x} \right) + x\]


Find a particular solution of the following differential equation:- (x + y) dy + (x − y) dx = 0; y = 1 when x = 1


Find the equation of a curve passing through the point (0, 0) and whose differential equation is \[\frac{dy}{dx} = e^x \sin x.\]


Solve the differential equation : `("x"^2 + 3"xy" + "y"^2)d"x" - "x"^2 d"y" = 0  "given that"  "y" = 0  "when"  "x" = 1`.


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


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


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


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


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


Solution of the differential equation tany sec2xdx + tanx sec2ydy = 0 is ______.


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


The solution of `x ("d"y)/("d"x) + y` = ex is ______.


The solution of the equation (2y – 1)dx – (2x + 3)dy = 0 is ______.


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


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


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


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


The solution of the differential equation ydx + (x + xy)dy = 0 is ______.


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


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 ______.


Find the general solution of the differential equation `x (dy)/(dx) = y(logy - logx + 1)`.


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×