Q. 13

# If sin x is an integrating factor of the differential equation dy/dx + Py = Q, then write the value of P.

Answer :

Since is a linear differential equation

Integrating factor = e^{∫ p dx} = sin x (Given)

Taking log both sides we get,

⇒ log (e^{∫ p dx}) = log (sin x)

⇒ ∫ p dx log (e)= log (sin x)

⇒ ∫ p dx = log (sin x) ∵ log (e) = 1

Differentiate w.r.t x we get,

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