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.
Stacey Warren - Expert brainly.com
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this has to do with continuity right?
i think that's the point of it, yeah
....since u' is continuous at t=1; then that implies that u is continuos and exists at yada yada yada right?
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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
is it enough? dunno, id say yes, but proofs are never my strong point :)
i'm pretty sure those are the criteria, so i would assume it proves it, but just wanted to make sure that sounded right