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anonymous
 5 years ago
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.
anonymous
 5 years ago
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.

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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0this has to do with continuity right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i think that's the point of it, yeah

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0....since u' is continuous at t=1; then that implies that u is continuos and exists at yada yada yada right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0would 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 ?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0is it enough? dunno, id say yes, but proofs are never my strong point :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i'm pretty sure those are the criteria, so i would assume it proves it, but just wanted to make sure that sounded right
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