Solution of differential equation x ,dy - y ,dx = 0 represents - Vidyadip

MCQ

Solution of differential equation $x\,dy - y\,dx = 0$ represents

A
Rectangular hyperbola
✓
Straight line passing through origin
C
Parabola whose vertex is at origin
D
Circle whose centre is at origin

✓

Answer

Correct option: B.

Straight line passing through origin

b
(b) $ydx - xdy = 0$ ==> $\frac{1}{x}dx = \frac{1}{y}dy$

On integrating, $\log x = \log y + \log c$

==> $\log \frac{x}{y} = \log c$ ==> $x = cy$

It is a straight line passing through origin.

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