i am curious why following initial-value problem
$ \frac{dy}{dt}=\frac{1}{y},\quad y(0)=0$ has no solution
if we solve it by method of seperation of variables, we get that
$y(t)=\pm\sqrt{2t\ {}} $
we have assumption that our function has form $f(t,y)$; book from which i have taken this example,says that ,it has not solution because of it does not contain $t$ variable (or at book language,does not include $t$ axis) i need to understand it well, as if i met such type of problem, i won't to mixes and say that,it has solution, thanks a lot of,as a additional fact, in book there is written,if change $y(0)=1$, then $y(t)=\sqrt{2t+1}$, it is defined on this interval $(-1/2,\infty)$, does it have solution here?if yes than, $2t$ would be defined on $[0,\infty]$ right? thanks