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Integrating Factor

Find the I....

Question

Find the $I . F$ of the differential equation:
${cos}^{2} x \frac{d y}{d x} + y = tan x$

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Solution

$\frac{d y}{d x} + y s e c^{2} x = t a n x . s e c^{2} x$

It is linear differential equation,

$I F = e^{\int s e c^{2} x d x}$

Therefore, $I F = e^{t a n x}$

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