anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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amistre64
  • amistre64
this has to do with continuity right?
anonymous
  • anonymous
i think that's the point of it, yeah
amistre64
  • amistre64
....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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anonymous
  • anonymous
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 ?
amistre64
  • amistre64
is it enough? dunno, id say yes, but proofs are never my strong point :)
anonymous
  • anonymous
i'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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