Maths. Section ADifferential Equations

The solution of the differential equation x dy - y dx = 0 represents

The solution of the differential equation $x\,dy - y\,dx = 0$ represents

Answer & explanation

Correct answer: option 1

The correct answer is Option (1) → straight line passing through origin

Separating the variables (for $x \ne 0, y \ne 0$):

$x\,dy = y\,dx$

$ \displaystyle \frac{dy}{y} = \frac{dx}{x} $

Integrating:

$\log|y| = \log|x| + \log|c|$
$y = cx$

For every value of c, $y = cx$ is a straight line through the origin.

NCERT Exemplar:
Differential Equations

$NCERT extract$