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I want to solve for $Y(x)$:

$$ Y(x) = A - Bx + C\ln(A/Y(x)) $$

where $A$, $B$, and $C$ are defined.

Not sure how to go about this. I'm tempted to treat $x$ and $Y(x)$ independently and solve them as roots, but I don't think that would be okay.

Gerry Myerson
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  • The answer is given in terms of Lambert's W-function. Is there a problem with the result, or are you asking about something else...? –  Dec 10 '13 at 21:30
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    In what sense is this a differential equation? And in what sense is this a Mathematica question? – m_goldberg Dec 10 '13 at 21:37

1 Answers1

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As told by Oleksandr R., the result is expressed in terms of Lambert's W function. The result is
y = c W(z) where z = a Exp[(a - b x) / c] / c.
You will find all the details of the transforms at
http://en.wikipedia.org/wiki/Lambert_W_function

Claude Leibovici
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