If Sinx is an integrating factor of the differential equation \frac{dy}{dx}+Py=Q, then P can be

  • Option 1)

    \log \:\sin x

  • Option 2)

    \cot x

  • Option 3)

    \sin x

  • Option 4)

    \log \: \cos x

 

Answers (1)

As learnt in

Linear Differential Equation -

\frac{dy}{dx}+Py= Q

- wherein

P, Q are functions of x alone.

 

 If e^{\int Pdx}= e ^{\log \sin x}\ \(given)

\Rightarrow \frac{d}{dx}\left ( \log \sin x \right ) = \frac{\cos x}{\sin x} = P = \cot x


Option 1)

\log \:\sin x

This option is incorrect

Option 2)

\cot x

This option is correct

Option 3)

\sin x

This option is incorrect

Option 4)

\log \: \cos x

This option is incorrect

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