[Maxima-bugs] [ maxima-Bugs-2014392 ] solve z = x*tanh(y) + y*tanh(x)

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Bugs item #2014392, was opened at 2008-07-09 18:25
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Category: Lisp Core - Solving equations
Group: None
Status: Open
Resolution: Rejected
Priority: 5
Private: No
Submitted By: Nobody/Anonymous (nobody)
Assigned to: Nobody/Anonymous (nobody)
Summary: solve z = x*tanh(y) + y*tanh(x)

Initial Comment:
solve([z=x*tanh(y)+tanh(x)*y], [y]);

returns

[y=-(x*tanh(y)-z)/tanh(x)]

Which has y on both sides of the equation

Why can Maxima not solve this equation ? (or if there is no solution is return an error)

I believe that if z and x have fixed values, then y can be determined.


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Comment By: Nobody/Anonymous (nobody)
Date: 2008-08-17 18:56

Message:
Logged In: NO 

Thank you for your feedback, it was quite helpful.

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Comment By: Stavros Macrakis (macrakis)
Date: 2008-07-17 14:03

Message:
Logged In: YES 
user_id=588346
Originator: NO

This is a transcendental equation which does not have a solution in closed
form in the usual elementary functions.  That is true of the simpler
equations y=tanh(y), y=exp(y), etc. Remember that Maxima's solve command
finds exact solutions, not approximations.

Of course, for fixed z and x, you can find a numerical approximation. 
Take a look at the documentation for find_root. Example:

     find_root(y=tanh(y)+1,y,0,10);
     1.961179751371539



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Comment By: Nobody/Anonymous (nobody)
Date: 2008-07-09 18:34

Message:
Logged In: NO 

plot3d(x*tanh(y)+tanh(x)*y, [x,-5,5], [y,-5,5], [plot_format,openmath])$

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