For 0 < x < π, what is the general solution of dy/dx + ycot x = cosec x?

Question 110

MediumOriginal question

For $0 < x < \pi$ , what is the general solution of $\frac{dy}{dx} + y\cot x = \operatorname{cosec} x$ ?

y = (x + C)\operatorname{cosec} x

Correct answerYour answer

y = (x + C)\sin x

Correct answerYour answer

y = x + C\operatorname{cosec} x

Correct answerYour answer

y = x\operatorname{cosec} x + C

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

The factor is $e^{\int \cot x\,dx} = \sin x$ , and $\operatorname{cosec} x \cdot \sin x = 1$ .
$y\sin x = \int 1\,dx = x + C$ , so $y = (x + C)\operatorname{cosec} x$ .

Worth noting

$(x + C)\sin x$ multiplies by the factor $\sin x$ where it should divide by it.

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