हिंदी

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

Advertisements
Advertisements

प्रश्न

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

विकल्प

  • 0

  • 2

  • 3

  • 4

MCQ

उत्तर

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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 22: Differential Equations - MCQ [पृष्ठ १४३]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 22 Differential Equations
MCQ | Q 43 | पृष्ठ १४३

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Find the differential equation representing the curve y = cx + c2.


Find the particular solution of differential equation:

`dy/dx=-(x+ycosx)/(1+sinx) " given that " y= 1 " when "x = 0`


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 log(dy/dx)= 3x + 4y, given that y = 0 when x = 0.


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

y = Ax : xy′ = y (x ≠ 0)


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)`


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


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


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


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


cos (x + y) dy = dx


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


`y sec^2 x + (y + 7) tan x(dy)/(dx)=0`


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


x2 dy + (x2 − xy + y2) dx = 0


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


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


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


For the following differential equation, find the general solution:- `y log y dx − x dy = 0`


Solve the following differential equation:-

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


Solve the following differential equation:-

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


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


Find the equation of a curve passing through the point (0, 1). If the slope of the tangent to the curve at any point (x, y) is equal to the sum of the x-coordinate and the product of the x-coordinate and y-coordinate of that point.


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


If y(x) is a solution of `((2 + sinx)/(1 + y))"dy"/"dx"` = – cosx and y (0) = 1, then find the value of `y(pi/2)`.


Solve: `2(y + 3) - xy "dy"/"dx"` = 0, given that y(1) = – 2.


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


Solve the differential equation (1 + y2) tan–1xdx + 2y(1 + x2)dy = 0.


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


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


Integrating factor of `(x"d"y)/("d"x) - y = x^4 - 3x` is ______.


The solution of `("d"y)/("d"x) + y = "e"^-x`, y(0) = 0 is ______.


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


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:

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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×