If sinx is an intergrating factor of the differential equation dydx+Py=Q, then P can be

Given dydx+py=QI.F=e∫p dx⇒ e∫p dx= sinx⇒∫p dx=log(sinx)diff w.r. to x⇒ p= 1sinx.cosx= cotx

If sinx is an intergrating factor of the differential equation dydx+Py=Q, then P can be

Given dydx+py=QI.F=e∫p dx⇒ e∫p dx= sinx⇒∫p dx=log(sinx)diff w.r. to x⇒ p= 1sinx.cosx= cotx

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

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log sinx

cot x

sin x

log cos x

answer is B.

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Detailed Solution

$\begin{array}{l} G i v e n \frac{d y}{d x} + p y = Q \\ I . F = e^{\int p d x} \\ \Rightarrow e^{\int p d x} = \sin x \\ \Rightarrow \int p d x = \log (\sin x) \\ d i f f w . r . t o x \\ \Rightarrow p = \frac{1}{\sin x} . \cos x \\ = \cot x \end{array}$