# Unable to solve equation explicitely

I have the following equation:

```
U=(8*pi*h*f^3)/(c^3)/(exp((h*f)/(k*T))-1),
```

and I would like to solve it's derivative with respect to f equal to zero for f. I know this equation can be explicitly solved for f with the LambertW function, however sage only provides an implicit solution, or if I specify it must be explicit, it only gives the trivial solution. Is there any way to get it to use the LambertW function when using solve?

Edited for legibility : to quote code, indent it by four spaces...

For the benefit of future commenters/answerers, a bit of Sage code :

Sage gives indeed an implicit answer :

Neither Sympy, Giac nor Fricas can solve this one.Mathematica gives an explicit answer using Lambert's W :

ProductLog being indeed Marhematica's name for Lambert's W.

HTH,

It is easy to solve the equation manually using the definition of Lambert W function.