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Question

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


A
y=ktanx
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B
y=kcscx
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C
y=ksinx
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D
y=kcosx
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Solution

The correct option is A $$y=k\sin x$$
$$\dfrac{dy}{dx}=y \cot x$$
$$\Rightarrow \dfrac{dy}{y}= \cot x dx$$
$$\Rightarrow \dfrac{dy}{y} = \dfrac{\cos x}{\sin x} dx$$
$$\Rightarrow ln |y|+ln |c|= ln |\sin x|$$
$$\Rightarrow ln |Cy| = ln |\sin \, x|$$
$$\Rightarrow cy= \sin x$$
$$\Rightarrow y= k \sin x$$ where k= constant

Mathematics

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