Solution of the differential equation $x\, dy - y\, dx = 0 $ represents
Answer & explanation
Correct answer: option 2
The correct answer is option (2) : a straight line passing through the origin
We have,
$x\, dy - y \, dx = 0 $
$⇒\frac{1}{y}dy-\frac{1}{x}dx=0$
$⇒log\, y - log\, x - log\, C$ {On integrating]
$⇒\frac{y}{x}= C⇒y = Cx $
Clearly, it represents a straight line passing through the origin.