Advertisements
Advertisements
प्रश्न
The number of arbitrary constants in the particular solution of a differential equation of third order are ______.
पर्याय
3
2
1
0
Advertisements
उत्तर
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.
APPEARS IN
संबंधित प्रश्न
Solve the differential equation cos(x +y) dy = dx hence find the particular solution for x = 0 and y = 0.
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`
If `y=sqrt(sinx+sqrt(sinx+sqrt(sinx+..... oo))),` then show that `dy/dx=cosx/(2y-1)`
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
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y – cos y = x : (y sin y + cos y + x) y′ = y
Find the differential equation of the family of concentric circles `x^2 + y^2 = a^2`
The population of a town grows at the rate of 10% per year. Using differential equation, find how long will it take for the population to grow 4 times.
The general solution of the differential equation \[\frac{dy}{dx} + y \] cot x = cosec x, is
The solution of the differential equation \[\frac{dy}{dx} + \frac{2y}{x} = 0\] with y(1) = 1 is given by
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
\[\frac{dy}{dx} = \frac{\sin x + x \cos x}{y\left( 2 \log y + 1 \right)}\]
(1 + y + x2 y) dx + (x + x3) dy = 0
(x2 + 1) dy + (2y − 1) dx = 0
`(2ax+x^2)(dy)/(dx)=a^2+2ax`
x2 dy + (x2 − xy + y2) dx = 0
\[\frac{dy}{dx} + 2y = \sin 3x\]
\[\cos^2 x\frac{dy}{dx} + y = \tan x\]
Solve the differential equation:
(1 + y2) dx = (tan−1 y − x) dy
Find the general solution of the differential equation \[\frac{dy}{dx} = \frac{x + 1}{2 - y}, y \neq 2\]
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:- \[\frac{dy}{dx} = \left( 1 + x^2 \right)\left( 1 + y^2 \right)\]
Solve the following differential equation:-
(1 + x2) dy + 2xy dx = cot x dx
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 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.
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 sec x` = tan x is y(secx – tanx) = secx – tanx + x + k.
If y(t) is a solution of `(1 + "t")"dy"/"dt" - "t"y` = 1 and y(0) = – 1, then show that y(1) = `-1/2`.
Find the general solution of y2dx + (x2 – xy + y2) dy = 0.
The general solution of ex cosy dx – ex siny dy = 0 is ______.
The integrating factor of the differential equation `("d"y)/("d"x) + y = (1 + y)/x` is ______.
The general solution of the differential equation `("d"y)/("d"x) = "e"^(x^2/2) + xy` is ______.
General solution of `("d"y)/("d"x) + y` = sinx is ______.
The solution of differential equation coty dx = xdy is ______.
The solution of the differential equation `("d"y)/("d"x) = (x + 2y)/x` is x + y = kx2.
Which of the following differential equations has `y = x` as one of its particular solution?
Find the general solution of the differential equation:
`log((dy)/(dx)) = ax + by`.
Find the general solution of the differential equation:
`(dy)/(dx) = (3e^(2x) + 3e^(4x))/(e^x + e^-x)`
Solve the differential equation:
`(xdy - ydx) ysin(y/x) = (ydx + xdy) xcos(y/x)`.
Find the particular solution satisfying the condition that y = π when x = 1.
