The DE is of the type 'with separable variables' , so that its solution can be found in 'standard way' ...

(1)

... and taking into account the 'initial conditions' we have...

(2)

It is evident from (2) that u(*) has a singularity in and this fact is confirmed if we expand u(*) in series around ...

(3)

... which converges for . So the value of You are searching is ...

Kind regards