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mathlilly
 3 years ago
Show by verifying the hypothesis of the Existence and Uniqueness Theorem that the initial value problem x dot = 1+x^2, x(0) = 0 has a unique solution. Find the solution. what is the maximal interval of definition of the solution? I'll put what I think is the answer as a response. Could you tell me if I took the right approach?
mathlilly
 3 years ago
Show by verifying the hypothesis of the Existence and Uniqueness Theorem that the initial value problem x dot = 1+x^2, x(0) = 0 has a unique solution. Find the solution. what is the maximal interval of definition of the solution? I'll put what I think is the answer as a response. Could you tell me if I took the right approach?

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mathlilly
 3 years ago
Best ResponseYou've already chosen the best response.0Because f: R> R is continuous, then for any x knot which is an element of R, there is an interval (alpha,beta) containing 0 and there is a solution x(t) of x dot = f(x). The limit exist, therefore a solution exists. Because f is differentiable and f' is continuous, then x(t) is unique.

mathlilly
 3 years ago
Best ResponseYou've already chosen the best response.0The solution is 0 and the maximal interval of definition is (infinity,infinity)
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