the function 'solve' doesn't give all the solutions.

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Richard
Richard 2013-10-9
评论： Richard 2013-10-10
% this does not give all the solutions
syms u;
solve(1-0.99-(u+1)*exp(-u));
double(ans)
see the short 3-line code there, try it out.
The solutions should be u1=-0.996308, and u2=6.63835
But this code only gives me u1, and mentions nothing about u2.
Can any one tells me why or which function should I use to get all the answers.
Thanks!
  2 个评论
Roger Stafford
Roger Stafford 2013-10-9
My very ancient version of 'solve' gives both your solutions. I don't know why your version should give only one of them.
Walter Roberson
Walter Roberson 2013-10-9
I have noticed the MuPAD's solve() seems to have difficulty in finding solutions involving LambertW.

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Friedrich
Friedrich 2013-10-9
编辑：Friedrich 2013-10-9
Hi,
seems like you are interested in real solutions only. So use:
>> solve(1-0.99-(u+1)*exp(-u),'Real',true)
ans =
- lambertw(0, -exp(-1)/100) - 1
- lambertw(-1, -exp(-1)/100) - 1
If you dont set Real to true MATLAB solves it Complex which would give an infinite amount of solutions. When you use MuPAD Notepad you will obtain:
So only k=0 and k =-1 give Real solutions.
UPDATE: Since you want real solutions only its might be better to use a numeric solver:
>> feval(symengine,'numeric::solve','1-0.99-(u+1)*exp(-u)','AllRealRoots')
ans =
[ [u == -0.99630759688740599414645321772374], [u == 6.6383520679938122693712394050244]]
  1 个评论
Richard
Richard 2013-10-10
编辑：Richard 2013-10-10
Yes. You are right. I am only interested in the real solutions. I use this occasionally when I don't have an equations solver. But when I have internet access, I also like to use Wolfram Alpha. It is a cool online mathematics tool! Thanks so much for your help and information, Friedrich!

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