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What are all solutions to the differential equation

$$ u'(x)v(x) + u(x)v'(x) = u'(x)v'(x) $$

Where the derivative is with respect to $x$.

mick
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    What are your thoughts on the problem? Is there any particular motivation for this problem? – Ben Grossmann Jul 28 '17 at 14:05
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    So $v$ is known and you want to solve for $u$? If you change to $U = \log u - x$ and $V = \log v - x$ then we have $U'V' = 1$. – Winther Jul 28 '17 at 14:09
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    see here https://math.stackexchange.com/questions/10927/when-do-the-freshmans-dream-product-and-quotient-rules-for-differentiation-hold?rq=1 – Wintermute Jul 28 '17 at 14:10

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