The solution of the differential equation xdy + ydx = 0 is:

Question

The solution of the differential equation xdy + ydx = 0 is: (A) xy = c (B) x2 + y2 = c (C) xy log x = 1 (D) log xy = c

Tardigrade Admin · Accepted Answer

Given, xdy + ydx = 0 Divide both sides above equation by xy, We get, (dx/dy) + (dy/y) = 0 Integrating it on both sides, we get log x + log y = log c ⇒ log xy = log c ⇒ xy = c.

Q. The solution of the differential equation xdy + ydx = 0 is:

xy = c

$x^{2} + y^{2} = c$

xy log x = 1

log xy = c

Given, xdy + ydx = 0
Divide both sides above equation by xy,
We get, $\frac{d x}{d y} + \frac{d y}{y} = 0$
Integrating it on both sides, we get
log x + log y = log c
$\Rightarrow$ log xy = log c $\Rightarrow$ xy = c.