Advertisements
Advertisements
Question
Solution of differential equation xdy – ydx = 0 represents : ______.
Options
A rectangular hyperbola
Parabola whose vertex is at origin
Straight line passing through origin
A circle whose centre is at origin
Advertisements
Solution
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
RELATED QUESTIONS
Solve the differential equation: `x+ydy/dx=sec(x^2+y^2)` Also find the particular solution if x = y = 0.
If x = Φ(t) differentiable function of ‘ t ' then prove that `int f(x) dx=intf[phi(t)]phi'(t)dt`
Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.
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 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 = Ax : xy′ = y (x ≠ 0)
The number of arbitrary constants in the particular solution of a differential equation of third order are ______.
if `y = sin^(-1) (6xsqrt(1-9x^2))`, `1/(3sqrt2) < x < 1/(3sqrt2)` then find `(dy)/(dx)`
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 x2 + y2 \[\frac{dy}{dx}\]= 4, is
The solution of the differential equation x dx + y dy = x2 y dy − y2 x dx, is
The solution of the differential equation \[\frac{dy}{dx} - ky = 0, y\left( 0 \right) = 1\] approaches to zero when x → ∞, if
The general solution of the differential equation \[\frac{dy}{dx} = e^{x + y}\], is
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
Solve the differential equation (x2 − yx2) dy + (y2 + x2y2) dx = 0, given that y = 1, when x = 1.
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
\[\frac{dy}{dx} - y \tan x = e^x\]
`y sec^2 x + (y + 7) tan x(dy)/(dx)=0`
x2 dy + (x2 − xy + y2) dx = 0
\[\left( 1 + y^2 \right) + \left( x - e^{- \tan^{- 1} y} \right)\frac{dy}{dx} = 0\]
`2 cos x(dy)/(dx)+4y sin x = sin 2x," given that "y = 0" when "x = pi/3.`
For the following differential equation, find the general solution:- \[\frac{dy}{dx} + y = 1\]
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:- `y dx + x log (y)/(x)dy-2x dy=0`
Solve the following differential equation:-
\[\frac{dy}{dx} - y = \cos x\]
Solve the following differential equation:-
\[x \log x\frac{dy}{dx} + y = \frac{2}{x}\log x\]
Find a particular solution of the following differential equation:- \[\left( 1 + x^2 \right)\frac{dy}{dx} + 2xy = \frac{1}{1 + x^2}; y = 0,\text{ when }x = 1\]
Find the general solution of `"dy"/"dx" + "a"y` = emx
If y(x) is a solution of `((2 + sinx)/(1 + y))"dy"/"dx"` = – cosx and y (0) = 1, then find the value of `y(pi/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`.
The general solution of ex cosy dx – ex siny dy = 0 is ______.
The general solution of `("d"y)/("d"x) = 2x"e"^(x^2 - y)` 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 the differential equation of the type `("d"x)/("d"x) + "P"_1x = "Q"_1` is given by ______.
The solution of differential equation coty dx = xdy is ______.
Number of arbitrary constants in the particular solution of a differential equation of order two is two.
Find a particular solution satisfying the given condition `- cos((dy)/(dx)) = a, (a ∈ R), y` = 1 when `x` = 0
