help with dy/dx + 4xy - (cos x / e^2x^2) =0

aldo101

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May 20, 2007
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4
I got a sample test and I am having problems with this question.

dy/dx + 4xy - (cos x / e^2x^2) =0

Thank you.
 
Rewrite: \(\displaystyle \L\ \frac{dy}{dx}\ + 4xy = (\frac{cosx}{e^{2x^2}}\)\)

Take your integrating factor, \(\displaystyle \L\ e^{2x^2}\)

Hence, \(\displaystyle \L\ \frac{d}{dx}\ (y e^{2x^2}) = cosx\)

And, integrating: \(\displaystyle \L\ y e^{2x^2} = sinx + C\)

Therefore: \(\displaystyle \L\ y = sinx e^{-2x^2} + Ce^{-2x^2}\)

\(\displaystyle \L\ = e^{-2x^2}(sinx + C)\)
 
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