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