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Any tips, useful links or solutions and an explanation would be greatly appreciated!

Thanks!

- Thread starter MathewsMD
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- #1

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Any tips, useful links or solutions and an explanation would be greatly appreciated!

Thanks!

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:(

10char

10char

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In a lot of situations, it's not necessary to get analytic solutions. What is this for?

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HallsofIvy

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Well, when we have these mixed exponential equations, we try to put it in Lambert-W form. That is, in the form:

Any tips, useful links or solutions and an explanation would be greatly appreciated!

Thanks!

[tex]g(x,y)e^{g(x,y)}=h(x)[/tex]

Then by definition of the Lambert W function which you can look up, we take the W function of both sides and obtain:

[tex]g(x,y)=W(h)[/tex]

Now, doing a little moving around of your equation:

[tex]1/2 e^y=2x-3/2-y[/tex]

[tex]1/2 e^{2x-3/2}=e^{-y} e^{2x-3/2}(2x-3/2-y)[/tex]

or:

[tex](2x-3/2-y)e^{2x-3/2-y}=1/2 e^{2/x-3/2}[/tex]

I'll let you finish it to isolate y in terms of the perfectly valid (multi-valued) function of x in terms of the Lambert W-function.

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