The solution of differential equation dy dx + ^2 y = 0 is - Vidyadip

MCQ

The solution of differential equation $\frac{{dy}}{{dx}} + {\sin ^2}y = 0$ is

A
$y + 2\cos y = c$
B
$y - 2\sin y = c$
✓
$x = \cot y + c$
D
$y = \cot x + c$

✓

Answer

Correct option: C.

$x = \cot y + c$

c
(c) $\frac{{dy}}{{dx}} + {\sin ^2}y = 0$ ==> $ - \frac{{dy}}{{{{\sin }^2}y}} = dx$.

On integrating, we get $x = \cot y + c$.

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