u'=u^2
u(0)=1
find >0 s.t. the solution exists
hint?
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