Advertisements
Advertisements
Question
The number of arbitrary constants in the particular solution of a differential equation of third order are ______.
Options
3
2
1
0
Solution
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
RELATED QUESTIONS
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 x (1 + y2) dx – y (1 + x2) dy = 0, given that y = 1 when x = 0.
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y = ex + 1 : y″ – y′ = 0
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
`y sqrt(1 + x^2) : y' = (xy)/(1+x^2)`
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)`
Solve the differential equation `[e^(-2sqrtx)/sqrtx - y/sqrtx] dx/dy = 1 (x != 0).`
If y = etan x+ (log x)tan x then find dy/dx
The general solution of the differential equation \[\frac{dy}{dx} + y \] cot x = cosec x, is
The solution of the differential equation \[2x\frac{dy}{dx} - y = 3\] represents
The solution of the differential equation \[x\frac{dy}{dx} = y + x \tan\frac{y}{x}\], is
The solution of the differential equation \[\frac{dy}{dx} + 1 = e^{x + y}\], is
Find the general solution of the differential equation \[x \cos \left( \frac{y}{x} \right)\frac{dy}{dx} = y \cos\left( \frac{y}{x} \right) + x .\]
Find the particular solution of the differential equation `(1+y^2)+(x-e^(tan-1 )y)dy/dx=` given that y = 0 when x = 1.
Write the solution of the differential equation \[\frac{dy}{dx} = 2^{- y}\] .
Find the particular solution of the differential equation \[\frac{dy}{dx} = \frac{x\left( 2 \log x + 1 \right)}{\sin y + y \cos y}\] given that
\[\frac{dy}{dx} = \frac{\sin x + x \cos x}{y\left( 2 \log y + 1 \right)}\]
`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 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:-
\[x\frac{dy}{dx} + 2y = x^2 , x \neq 0\]
Solve the following differential equation:-
\[\left( x + y \right)\frac{dy}{dx} = 1\]
Solve the following differential equation:-
\[\left( x + 3 y^2 \right)\frac{dy}{dx} = y\]
Find a particular solution of the following differential equation:- (x + y) dy + (x − y) dx = 0; y = 1 when x = 1
Solution of the differential equation `"dx"/x + "dy"/y` = 0 is ______.
Find the general solution of `("d"y)/("d"x) -3y = sin2x`
If y = e–x (Acosx + Bsinx), then y is a solution of ______.
Solution of differential equation xdy – ydx = 0 represents : ______.
Solution of the differential equation tany sec2xdx + tanx sec2ydy = 0 is ______.
Solution of `("d"y)/("d"x) - y` = 1, y(0) = 1 is given by ______.
The number of solutions of `("d"y)/("d"x) = (y + 1)/(x - 1)` when y (1) = 2 is ______.
tan–1x + tan–1y = c is the general solution of the differential equation ______.
The general solution of ex cosy dx – ex siny dy = 0 is ______.
The general solution of the differential equation `("d"y)/("d"x) = "e"^(x^2/2) + xy` is ______.
The differential equation for which y = acosx + bsinx is a solution, is ______.
General solution of the differential equation of the type `("d"x)/("d"x) + "P"_1x = "Q"_1` is given by ______.
The member of arbitrary constants in the particulars solution of a differential equation of third order as
Find the particular solution of the differential equation `x (dy)/(dx) - y = x^2.e^x`, given y(1) = 0.
The differential equation of all parabolas that have origin as vertex and y-axis as axis of symmetry is ______.
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.