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Solution of the differential equation $x\, dy - y\, dx = 0 $ represents |
a rectangular hyperbola a straight line passing through the origin parabola whose vertex is at origin circle whose centre is at the origin |
a straight line passing through the origin |
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. |
