u'=u^2

u(0)=1

find >0 s.t. the solution exists

hint?

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- November 7th 2009, 02:07 PMNuscExistence
u'=u^2

u(0)=1

find >0 s.t. the solution exists

hint? - November 7th 2009, 08:05 PMchisigma
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

- November 7th 2009, 08:31 PMNusc