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Does the function f(t, u) = t|u| satisfy the Lipschitz condition for t on a closed...

Does the function f(t, u) = t|u| satisfy the Lipschitz condition for t on a closed and limited interval J.

Is there a unique solution for u' = f(t,u) , u(0) = b , for all t ∈ R where b ∈ R, if yes, find the solution.

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