Advertisements
Advertisements
प्रश्न
The number of arbitrary constants in the particular solution of a differential equation of third order is
पर्याय
3
2
1
0
Advertisements
उत्तर
0
The number of arbitrary constants in the particular solution of a differential equation is always zero.
APPEARS IN
संबंधित प्रश्न
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 x = Φ(t) differentiable function of ‘ t ' then prove that `int f(x) dx=intf[phi(t)]phi'(t)dt`
Find the particular solution of differential equation:
`dy/dx=-(x+ycosx)/(1+sinx) " given that " y= 1 " when "x = 0`
Find a particular solution of the differential equation`(x + 1) dy/dx = 2e^(-y) - 1`, given that y = 0 when x = 0.
If y = etan x+ (log x)tan x then find dy/dx
Write the order of the differential equation associated with the primitive y = C1 + C2 ex + C3 e−2x + C4, where C1, C2, C3, C4 are arbitrary constants.
The solution of the differential equation \[2x\frac{dy}{dx} - y = 3\] represents
The solution of the differential equation \[\left( 1 + x^2 \right)\frac{dy}{dx} + 1 + y^2 = 0\], is
The solution of the differential equation \[\frac{dy}{dx} = \frac{x^2 + xy + y^2}{x^2}\], is
The general solution of the differential equation \[\frac{y dx - x dy}{y} = 0\], is
Find the general solution of the differential equation \[x \cos \left( \frac{y}{x} \right)\frac{dy}{dx} = y \cos\left( \frac{y}{x} \right) + x .\]
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
x (e2y − 1) dy + (x2 − 1) ey dx = 0
\[\frac{dy}{dx} + 1 = e^{x + y}\]
\[\frac{dy}{dx} + \frac{y}{x} = \frac{y^2}{x^2}\]
(x + y − 1) dy = (x + y) dx
(1 + y + x2 y) dx + (x + x3) dy = 0
\[x\frac{dy}{dx} + x \cos^2 \left( \frac{y}{x} \right) = y\]
`2 cos x(dy)/(dx)+4y sin x = sin 2x," given that "y = 0" when "x = pi/3.`
Find the general solution of the differential equation \[\frac{dy}{dx} = \frac{x + 1}{2 - y}, y \neq 2\]
For the following differential equation, find the general solution:- \[\frac{dy}{dx} = \left( 1 + x^2 \right)\left( 1 + y^2 \right)\]
For the following differential equation, find the general solution:- `y log y dx − x dy = 0`
Solve the following differential equation:- \[\left( x - y \right)\frac{dy}{dx} = x + 2y\]
Solve the following differential equation:- `y dx + x log (y)/(x)dy-2x dy=0`
Solve the following differential equation:-
\[\frac{dy}{dx} - y = \cos x\]
Find a particular solution of the following differential equation:- x2 dy + (xy + y2) dx = 0; y = 1 when x = 1
Solution of the differential equation `"dx"/x + "dy"/y` = 0 is ______.
The general solution of the differential equation `"dy"/"dx" + y sec x` = tan x is y(secx – tanx) = secx – tanx + x + k.
Find the general solution of `(x + 2y^3) "dy"/"dx"` = y
The differential equation for y = Acos αx + Bsin αx, where A and B are arbitrary constants is ______.
Solution of differential equation xdy – ydx = 0 represents : ______.
Integrating factor of `(x"d"y)/("d"x) - y = x^4 - 3x` is ______.
tan–1x + tan–1y = c is the general solution of the differential equation ______.
The solution of `("d"y)/("d"x) + y = "e"^-x`, y(0) = 0 is ______.
The differential equation for which y = acosx + bsinx is a solution, is ______.
The general solution of the differential equation (ex + 1) ydy = (y + 1) exdx is ______.
The number of arbitrary constants in the general solution of a differential equation of order three is ______.
The solution of the differential equation ydx + (x + xy)dy = 0 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 particular solution of the following differential equation, given that y = 0 when x = `pi/4`.
`(dy)/(dx) + ycotx = 2/(1 + sinx)`
