[aprescott]

Isn't the purpose of the example to make it hard to just trivially deduce y? If you know y = 1/(1 - t) then yeah it's undefined at t = 1. The example given doesn't seem to lend itself to that though, and a lesson is to know when your tooling isn't good enough.

[JustFinishedBSG]

But if v' > u' with v(0) = u(0) and u blows up then we know that v blows up. Because u blows up at 1 then we know that v will blow up at or before 1