How to solve following equation $a(x-2)e^x-c x-d=0$. I know that the equation like $a(x-2)e^x-d=0$ can solve using Lambert W function, but with this equation I'm confused, and I can solve.
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$\begingroup$ Any conditions for $a,c,d$ ? From a numerical point of view, the problem is interesting. $\endgroup$– Claude LeiboviciCommented Aug 3, 2018 at 15:12
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Assuming $c \neq 0$, write your equation as $$e^{-x}=\frac a c\, \frac{x-2}{ x+\frac dc}$$ and have a look at equation $(4)$ in this paper about the generalization of the Lambert $W$ function.
From a practical point of view, consider numerical methods.
answered Aug 3, 2018 at 14:23
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$\begingroup$ This is awesome. Exactly what I was looking for. Thanks. $\endgroup$– BonaCommented Aug 5, 2018 at 21:39