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-MFra-21-Topaz II
21-Topaz II
August 7, 2021
Solved

Disagreement between the calculated symbolic result and the numerical result (transcendent equation)

Good morning everyone,
how can I make the calculated value of the symbolic solution coincide with the numerical one of the given transcendent equation? (Imposing with the assumption that 20 <x <30 it falls into an endless loop )

I thank

trascendent.jpg

Werner_E
Werner_EAnswer
25-Diamond I
August 7, 2021

Would this help:

Werner_E_1-1628370294729.png

 

"fully" tries to force the symbolic to give ALL solutions of the equation and Mathcad tells us that we simply have to use all branches of the Labert-W function rather than just branch #0. Most branches gives you non-real results, but _n=-1 gives you the solution you are looking for.

 

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3 replies

AlanStevens19-Tanzanite
19-Tanzanite
August 7, 2021

See the following:

g0.png

 

Alan

 

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-MFra-21-Topaz IIAuthor
21-Topaz II
August 7, 2021

Yup! all clear, but I'm looking for the second root as a function of Lambert ...

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Werner_E
Werner_E25-Diamond IAnswer
25-Diamond I
August 7, 2021

Would this help:

Werner_E_1-1628370294729.png

 

"fully" tries to force the symbolic to give ALL solutions of the equation and Mathcad tells us that we simply have to use all branches of the Labert-W function rather than just branch #0. Most branches gives you non-real results, but _n=-1 gives you the solution you are looking for.

 

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