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Mathematics

OpenStudy (anonymous):

y dx + (2xy - e^(-2y) dy) = 0 solve using integrating factor

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OpenStudy (anonymous):

Divide by dy then y and rearrange: x'+2x=e^(-2y)/y Integrating factor: e^integral(2dy) = e^(2y) (x*e^(2y))' = e^(2y)*e^(-2y)/y = 1/y Integrate: x*e^(2y) = ln(y) + c Solution: x(y) = (ln(y) + c) * e^(-2y)

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