The general solution of the differential equation dy dx = x y is - Vidyadip

MCQ

The general solution of the differential equation $\frac{{dy}}{{dx}} = \cot x\cot y$ is

A
$\cos x = c\,\cos {\rm{ec}}y$
✓
$\sin x = c\sec y$
C
$\sin x = c\cos y$
D
$\cos x = c\sin y$

✓

Answer

Correct option: B.

$\sin x = c\sec y$

b
(b) $\frac{{dy}}{{dx}} = \cot x\cot y$ ==> $\int_{}^{} {\tan ydy = \int_{}^{} {\cot xdx} } $

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

==> $\sec y = c\sin x$or$c\sec y = \sin x$.

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