My Math Forum Integrating factor

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 May 13th, 2010, 08:41 AM #1 Newbie   Joined: May 2010 Posts: 12 Thanks: 0 Integrating factor I have this equation $y'+ytanx=sinx$. The integrating factor give me $f=\displaystyle\frac{e^x}{cosx}$ but remplacement in the equation and don't give me exact. Thanks
May 14th, 2010, 04:30 PM   #2
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Re: Integrating factor

Hello, asd!

Quote:
 $y\:'\:+\:y\,\tan x\;=\;\sin x$

$\text{Integrating factor: }\;I \;=\;e^{\int \tan x\,dx} \;=\; e^{-\ln|\cos x|} \;=\;e^{\ln|\sec x|} \;=\;\sec x$

$\text{Multiply: }\;\;y'\,\cdot\,\sec x \:+\:y\,\cdot\,\sec x\,\cdot\,\tan x \;=\;\sin x\,\cdot\,\sec x$

$\text{We have: }\;\;\frac{d}{dx}\bigg[y\,\cdot\,\sec x\bigg] \;\;=\;\tan x$

$\text{Integrate: }\;\;y\,\cdot\,\sec x \;\;=\;\;\ln|\sec x| \,+\,C$

$\text{Multiply by }\cos x:\;\; y \;\;=\;\;\cos x\,\cdot\,\ln|\sec x|\;+\;C\cos x$

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