Solution of differential equation xdy - ydx = 0 represents :

Question

Solution of differential equation xdy - ydx = 0 represents : (A) rectangular hyperbola (B) straight line passing through origin (C) parabola whose vertex is at origin (D) circle whose centre is at origin

Tardigrade Admin · Accepted Answer

x dy = ydx ( dy / y )=( dx / x ) ⇒ ℓ n y -ℓ n x = c y = kx ∴ straight line passing through origin

Q. Solution of differential equation $x d y - y d x = 0$ represents :

rectangular hyperbola

straight line passing through origin

parabola whose vertex is at origin

circle whose centre is at origin

$x d y = y d x$
$\frac{d y}{y} = \frac{d x}{x} \Rightarrow ℓ n y - ℓ n x = c$
$y = k x ∴$ straight line passing through origin

Q. Solution of differential equation xdy−ydx=0 represents :