Solve the following differential equations: dy dx + =0 - Vidyadip

Question

Solve the following differential equations:$\frac{\text{dy}}{\text{dx}}+\frac{\cos\text{x}\sin\text{y}}{\cos\text{y}}=0$

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Answer

$\frac{\text{dy}}{\text{dx}}+\frac{\cos\text{x}\sin\text{y}}{\cos\text{y}}=0$
$\frac{\text{dy}}{\text{dx}}=-\cos\text{x}\tan\text{y}$
$\frac{\text{dy}}{\tan\text{y}}=-\cos\text{x dx}$
$\int\cot\text{ y dy}=-\int\cos\text{x dx}$
$\log|\sin\text{y}|=-\sin\text{x + C}$
$\sin\text{x}+\log|\sin\text{y}|=\text{C}$

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