Question

Solve:
$\frac{dy}{dx}=y\cot x$

• A. $y=k\tan x$
• B. $y=k\csc x$
• C. $y=k\sin x$
• D. $y=k\cos x$

Answer 1

Answer: (C)

$y=k\sin x$

$\frac{dy}{dx}=y\cot x$

$\Rightarrow \frac{dy}{y}=\cot xdx$

$\Rightarrow \frac{dy}{y}=\frac{\cos x}{\sin x}dx$

$\Rightarrow ln|y|+ln|c|=ln|\sin x|$

$\Rightarrow ln|Cy|=ln|\sin x|$

$\Rightarrow cy=\sin x$

$\Rightarrow y=k\sin x$ where k= constant