Question

state explicitly how you know that the initial value problem u' = (t^2 + 1)u - t; u(1) = 3; has a unique solution valid in some interval containing t = 1.

Answer 1

this has to do with continuity right?

Answer 2

i think that's the point of it, yeah

Answer 3

....since u' is continuous at t=1; then that implies that u is continuos and exists at yada yada yada right?

Answer 4

would it be enough to use the existence theorem and take into account
1. that f(t, u) is continuous at t = 1, and
2. that the partial diff. eq. (u' = (t^2 + 1) - t) is also continuous in both u and t
?

Answer 5

is it enough? dunno, id say yes, but proofs are never my strong point :)

Answer 6

i'm pretty sure those are the criteria, so i would assume it proves it, but just wanted to make sure that sounded right