Advertisements
Advertisements
प्रश्न
The number of arbitrary constants in the general solution of a differential equation of order three is ______.
Advertisements
उत्तर
The number of arbitrary constants in the general solution of a differential equation of order three is 3.
Explanation:
Given that general solution of a differential equation has three arbitrary constants.
So we require three more equations to eliminate these three constants.
We can get three more equations by differentiating given equation three times.
So, the order of the differential equation is 3.
APPEARS IN
संबंधित प्रश्न
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
Find the general solution of the following differential equation :
`(1+y^2)+(x-e^(tan^(-1)y))dy/dx= 0`
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 = ex + 1 : y″ – y′ = 0
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
Solve the differential equation:
`e^(x/y)(1-x/y) + (1 + e^(x/y)) dx/dy = 0` when x = 0, y = 1
The solution of the differential equation \[\frac{dy}{dx} = 1 + x + y^2 + x y^2 , y\left( 0 \right) = 0\] is
Solution of the differential equation \[\frac{dy}{dx} + \frac{y}{x}=\sin x\] is
The solution of the differential equation \[\frac{dy}{dx} - ky = 0, y\left( 0 \right) = 1\] approaches to zero when x → ∞, if
The number of arbitrary constants in the general solution of differential equation of fourth order is
The general solution of the differential equation ex dy + (y ex + 2x) dx = 0 is
\[\frac{dy}{dx} = \frac{\sin x + x \cos x}{y\left( 2 \log y + 1 \right)}\]
(x + y − 1) dy = (x + y) dx
\[\frac{dy}{dx} - y \cot x = cosec\ x\]
\[\frac{dy}{dx} - y \tan x = - 2 \sin x\]
`y sec^2 x + (y + 7) tan x(dy)/(dx)=0`
\[\frac{dy}{dx} + y = 4x\]
Solve the differential equation:
(1 + y2) dx = (tan−1 y − x) dy
For the following differential equation, find the general solution:- \[\frac{dy}{dx} = \sqrt{4 - y^2}, - 2 < y < 2\]
Solve the following differential equation:-
\[\frac{dy}{dx} - y = \cos x\]
Solve the following differential equation:-
\[\frac{dy}{dx} + 2y = \sin x\]
Solve the following differential equation:-
(1 + x2) dy + 2xy dx = cot x dx
Find the equation of the curve passing through the point (1, 1) whose differential equation is x dy = (2x2 + 1) dx, x ≠ 0.
Solve the differential equation: `(d"y")/(d"x") - (2"x")/(1+"x"^2) "y" = "x"^2 + 2`
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`.
Solve:
`2(y + 3) - xy (dy)/(dx)` = 0, given that y(1) = – 2.
Integrating factor of `(x"d"y)/("d"x) - y = x^4 - 3x` is ______.
The solution of the differential equation cosx siny dx + sinx cosy dy = 0 is ______.
Which of the following is the general solution of `("d"^2y)/("d"x^2) - 2 ("d"y)/("d"x) + y` = 0?
General solution of `("d"y)/("d"x) + ytanx = secx` is ______.
The general solution of the differential equation (ex + 1) ydy = (y + 1) exdx is ______.
General solution of `("d"y)/("d"x) + y` = sinx is ______.
The solution of differential equation coty dx = xdy is ______.
The integrating factor of `("d"y)/("d"x) + y = (1 + y)/x` 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 a particular solution, satisfying the condition `(dy)/(dx) = y tan x ; y = 1` when `x = 0`
Find the general solution of the differential equation:
`(dy)/(dx) = (3e^(2x) + 3e^(4x))/(e^x + e^-x)`
The differential equation of all parabolas that have origin as vertex and y-axis as axis of symmetry is ______.
