Ok, so I have a nonlinear ODE:

y'=(y^2)+(t^2)+(t^2)(sin(t))^2

y is a function of t.

the problem sounds like this: Determine a non-trivial upper bound on the domain of existence for the forward solution with initial
condition y(0) = 0.


So basically I don't even understand the question. Should I find the solution and then search for the upper bound of this function? Maybe some hints how to do that?

Sorry for the sloppy writing.

Thanks.