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(1) Give an example of a 1-dimensional ODE of form x' = f(x), x(0)=x* where f: R->R is continuous but there exists more than one differentiable solution. Prove your assertion.

(2) Is it true that a 1-dimensional ODE of the same form as (1) where f(x) is differentiable in x for all x has a differential solution x(t) defined for all t>0? Why?