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I having trouble with this function:

$y=P_1+P_2x+P_3e^{P_4x}$

I would like to solve it in terms of x. This means I know $y, P_1, P_2, P_3$ and $P_4$ and I want to calculate $x$ by varying $y$ ($y$ is always positive in my system). I found another post, which is similar to my problem.

But I did not well understand how the Lambert $W$ function (assuming my function will requires this function) can be computed.

Gary
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andreberna
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1 Answers1

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Most computer algebra systems compute the $W$ function (defined by $x = W(x) e^{W(x)}$), it's Wikipedia page gives details on it's computation, and more detailed references.

No, there is no easy way out. Unfortunately. At least you can use a standard function in your solution, one that is well-known.

The GNU Scientific Library GSL includes a function that computes $W(x)$. It should be available on any Linux system, and probably as an add-on on MacOS and Windows.

vonbrand
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