The general solution of the differential equation e^y dy dx + ( e… - Vidyadip

MCQ

The general solution of the differential equation ${e^y}\frac{{dy}}{{dx}} + ({e^y} + 1)\cot x = 0$ is

A
$({e^y} + 1)\cos x = K$
B
$({e^y} + 1){\rm{cosec}}\,x = K$
✓
$({e^y} + 1)\sin x = K$
D
None of these

✓

Answer

Correct option: C.

$({e^y} + 1)\sin x = K$

c
(c) $\frac{{dy}}{{dx}} + \frac{{({e^y} + 1)\cot x}}{{{e^y}}} = 0$ ==> $\int_{}^{} {\frac{{{e^y}}}{{{e^y} + 1}}} dy + \int_{}^{} {\cot xdx} = 0$

==> $\log ({e^y} + 1) + \log \sin x = \log K$ ==> $({e^y} + 1)\sin x = K$.

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