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
Find the particular solution of the differential equation `e^xsqrt(1-y^2)dx+y/xdy=0` , given that y=1 when x=0
Solve the differential equation `dy/dx -y =e^x`
Solve the differential equation `[e^(-2sqrtx)/sqrtx - y/sqrtx] dx/dy = 1 (x != 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.`
Solve the differential equation `cos^2 x dy/dx` + y = tan x
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 \[\frac{dy}{dx} + 1 = e^{x + y}\], is
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
Which of the following differential equations has y = x as one of its particular solution?
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
(x2 + 1) dy + (2y − 1) dx = 0
Find the particular solution of the differential equation \[\frac{dy}{dx} = - 4x y^2\] given that y = 1, when x = 0.
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:- `y dx + x log (y)/(x)dy-2x dy=0`
Solve the following differential equation:-
y dx + (x − y2) dy = 0
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 equation of the curve passing through the point (1, 1) whose differential equation is x dy = (2x2 + 1) dx, x ≠ 0.
The general solution of the differential equation `"dy"/"dx" + y sec x` = tan x is y(secx – tanx) = secx – tanx + x + k.
Solve the differential equation dy = cosx(2 – y cosecx) dx given that y = 2 when x = `pi/2`
Solve the differential equation (1 + y2) tan–1xdx + 2y(1 + x2)dy = 0.
Find the general solution of `("d"y)/("d"x) -3y = sin2x`
If y = e–x (Acosx + Bsinx), then y is a solution of ______.
Integrating factor of the differential equation `cosx ("d"y)/("d"x) + ysinx` = 1 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 solution of `x ("d"y)/("d"x) + y` = ex is ______.
The solution of `("d"y)/("d"x) + y = "e"^-x`, y(0) = 0 is ______.
The solution of the differential equation `x(dy)/("d"x) + 2y = x^2` is ______.
Which of the following differential equations has `y = x` as one of its particular solution?
Find the particular solution of the differential equation `x (dy)/(dx) - y = x^2.e^x`, given y(1) = 0.
Find the general solution of the differential equation:
`(dy)/(dx) = (3e^(2x) + 3e^(4x))/(e^x + e^-x)`
The curve passing through (0, 1) and satisfying `sin(dy/dx) = 1/2` is ______.
If the solution curve of the differential equation `(dy)/(dx) = (x + y - 2)/(x - y)` passes through the point (2, 1) and (k + 1, 2), k > 0, then ______.
