Warning: Explicit solution could not be found. In solve at 81 ans = [ empty sym ]

Hello,

I have question about function solve. I would like to find r3. I have function like that:

f =1/(1/hext + r3/(hint*r1) + (r3*log(r2/r1))/k1 + (r3*log(r3/r2))/k2) - v

And i tried to do it like that:

>> syms r1 r2 r3 hint hext k1 k2 v

>> f = -v + 1/(((r3/(hint*r1))+(r3*log(r2/r1)/k1))+(r3*log(r3/r2)/k2)+(1/hext))

f = 1/(1/hext + r3/(hint*r1) + (r3*log(r2/r1))/k1 + (r3*log(r3/r2))/k2) - v

>> solve (f, r3)

Warning: Explicit solution could not be found.

> In solve at 81

ans =

[ empty sym ]

Do you have any ideas what's wrong?

Answer 1

[Roger Stafford]

By a certain trick my ancient version of ‘solve’ can find the solution to your problem which involves the ‘lambertw’ function. Perhaps this will work with your version also. The equations x = log(r3) and r3 = exp(x) are equivalent. Therefore everywhere in f that r3 occurs replace it with exp(x) and in log(r3/r2) replace that with the equivalent (x-log(r2)). You should then get this:

f = -v+1/(1/hext+exp(x)/(hint*r1)+(exp(x)*log(r2/r1))/k1+(exp(x)*(x-log(r2)))/k2);

Then solve for x. If you get a solution, as I did, then you can get an expression for r3 by taking the exponential function of x: r3 = exp(x).

In general, however, you should realize that there are a great many equations which ‘solve’ cannot find explicit solutions for. That is to be expected. Seeing the message “Warning: Explicit solution could not be found” does not mean that an error was made. It may simply be something ‘solve’ cannot find a solution to. Perhaps none is known in all of mathematics.

Answer 2

[Ma mate]

I don't know why but I have still the same result :( I have R2010a version of matlab if its important

>> syms r1 r2 x k1 k2 hint hext v

>> f = -v+1/(1/hext+exp(x)/(hint*r1)+(exp(x)*log(r2/r1))/k1+(exp(x)*(x-log(r2)))/k2)

f = 1/(1/hext + (log(r2/r1)*exp(x))/k1 + (exp(x)*(x - log(r2)))/k2 + exp(x)/(hint*r1)) - v

>> solve (f,x)

Warning: Explicit solution could not be found. > In solve at 81

ans =

[ empty sym ]

If it's no problem for you to give me your result should be perfect ! :)

[Roger Stafford]

For the expression

 f = -v+1/(1/hext+exp(x)/(hint*r1)+(exp(x)*log(r2/r1))/k1+(exp(x)*(x-log(r2)))/k2)

I obtained the rather horrendous solution

 x = lambertw(exp(-(-k1*k2-hint*r1*k2*log(r2)+hint*r1*k2*log(r1)+hint*r1*k1*log(r2))/k1/hint/r1)/v/hext*k2*(hext-v))-1/hint/r1*k2-1/k1*k2*log(r2)+1/k1*k2*log(r1)+log(r2)

Its ‘pretty’ version is:

lambertw(

        - k1 k2 - hint r1 k2 log(r2) + hint r1 k2 log(r1) + hint r1 k1 log(r2)
  exp(- ----------------------------------------------------------------------)
                                      k1 hint r1

                                k2     k2 log(r2)   k2 log(r1)
   k2 (hext - v)/(v hext)) - ------- - ---------- + ---------- + log(r2)
                             hint r1       k1           k1

Remember, however, that to get the solution for r3 you must take r3 = exp(x).

Answer 3

[Ma mate]

Thank you so much !