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

% 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!

[Roger Stafford]

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]

I have noticed the MuPAD's solve() seems to have difficulty in finding solutions involving LambertW.

Answer 1

[Friedrich]

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]]

[Richard]

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!