The differential equation y , ,dx = x , ,dy has a solution of the… - Vidyadip

MCQ

The differential equation $\cot y\,\,dx = x\,\,dy$ has a solution of the form

A
$y = \cos x$
✓
$x = c\sec y$
C
$x = \sin y$
D
$y = \sin x$

✓

Answer

Correct option: B.

$x = c\sec y$

b
(b) $\cot y.dx = x.dy$ ==> $\frac{{dx}}{x} = \frac{{dy}}{{\cot y}}$ ==> $\frac{{dx}}{x} = \tan y.dy$

Integrating both sides,

$\log x = \log \sec y + \log c$ ==> $x = c\sec y$.

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