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Question
What is integrating factor of \[\frac{dy}{dx}\] + y sec x = tan x?
Options
sec x + tan x
log (sec x + tan x)
esec x
sec x
Solution
sec x + tan x
We have,
\[\frac{dy}{dx} + y \sec x = \tan x\]
\[\text{ Comparing with }\frac{dy}{dx} + Py = Q, \text{ we get }\]
\[P = \sec x \]
\[Q = \tan x\]
Now,
\[I . F . = e^{\int\sec xdx} \]
\[ = e^{log\left( \sec x + \tan x \right)} \]
\[ = \sec x + \tan x\]
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