Advertisements
Advertisements
प्रश्न
Solution of differential equation xdy – ydx = 0 represents : ______.
विकल्प
A rectangular hyperbola
Parabola whose vertex is at origin
Straight line passing through origin
A circle whose centre is at origin
Advertisements
उत्तर
Solution of differential equation xdy – ydx = 0 represents : straight line passing through origin.
Explanation:
The given differential equation is xdy – ydx = 0
⇒ `("d"y)/("d"x) = y/x`
⇒ `("d"y)/y = ("d"x)/x`
Integrating both sides, we get
`int ("d"y)/y = ("d"x)/x`
⇒ log y = log x + log c
⇒ log y = log xc
⇒ y = xc
Which is a straight line passing through the origin.
APPEARS IN
संबंधित प्रश्न
Solve the differential equation cos(x +y) dy = dx hence find the particular solution for x = 0 and y = 0.
If `y=sqrt(sinx+sqrt(sinx+sqrt(sinx+..... oo))),` then show that `dy/dx=cosx/(2y-1)`
Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.
Find the particular solution of the differential equation dy/dx=1 + x + y + xy, given that y = 0 when x = 1.
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y = cos x + C : y′ + sin x = 0
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y = x sin x : xy' = `y + x sqrt (x^2 - y^2)` (x ≠ 0 and x > y or x < -y)
If y = etan x+ (log x)tan x then find dy/dx
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 solution of the differential equation \[x\frac{dy}{dx} = y + x \tan\frac{y}{x}\], 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 x dx + y dy = x2 y dy − y2 x dx, is
The solution of the differential equation \[\left( 1 + x^2 \right)\frac{dy}{dx} + 1 + y^2 = 0\], is
The number of arbitrary constants in the general solution of differential equation of fourth order is
(x + y − 1) dy = (x + y) dx
`y sec^2 x + (y + 7) tan x(dy)/(dx)=0`
x2 dy + (x2 − xy + y2) dx = 0
\[\cos^2 x\frac{dy}{dx} + y = \tan x\]
Solve the differential equation:
(1 + y2) dx = (tan−1 y − x) dy
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 the general solution:- \[\frac{dy}{dx} = \sqrt{4 - y^2}, - 2 < y < 2\]
Solve the following differential equation:- \[x \cos\left( \frac{y}{x} \right)\frac{dy}{dx} = y \cos\left( \frac{y}{x} \right) + x\]
Solve the following differential equation:-
\[\frac{dy}{dx} - y = \cos x\]
Solve the following differential equation:-
\[\frac{dy}{dx} + 3y = e^{- 2x}\]
Solve the following differential equation:-
\[\frac{dy}{dx} + \frac{y}{x} = x^2\]
Solve the following differential equation:-
(1 + x2) dy + 2xy dx = cot x dx
Solve the following differential equation:-
\[\left( x + y \right)\frac{dy}{dx} = 1\]
Find a particular solution of the following differential equation:- x2 dy + (xy + y2) dx = 0; y = 1 when x = 1
x + y = tan–1y is a solution of the differential equation `y^2 "dy"/"dx" + y^2 + 1` = 0.
Find the general solution of `"dy"/"dx" + "a"y` = emx
Solve:
`2(y + 3) - xy (dy)/(dx)` = 0, given that y(1) = – 2.
The number of solutions of `("d"y)/("d"x) = (y + 1)/(x - 1)` when y (1) = 2 is ______.
The solution of the differential equation cosx siny dx + sinx cosy dy = 0 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 ______.
The solution of differential equation coty dx = xdy is ______.
Find a particular solution satisfying the given condition `- cos((dy)/(dx)) = a, (a ∈ R), y` = 1 when `x` = 0
