The solution of $$cos$$⁡$$y+(x$$ siny −$$1)dydx=0$$ is xsecy $$=$$ Ptany $$+c$$ then ' P′ is

Introduction to Differential equations

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$The solution of \cos y + (x siny - 1) \frac{dy}{dx} = 0 is xsecy = Ptany + c then ' P^{'} is$

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Solution

$\begin{array}{l} \frac{dx}{dy} + xtany = secy \\ I.F. = e^{\int tany} = e^{\log \sec y} = secy \\ Solution of the differential equation is ysecy = \int \sec^{2} ydy = tany + c \\ ∴ P = 1 \end{array}$

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