probability theory – Criteria for the rigidity of the sequence of distribution functions

Leave $ φ_n $ Be a sequence of characteristic functions. We know that converge at each point of a not empty
open interval around 0
yet function $ φ which is also continued at 0.

Can you say that the sequence
of the distribution functions corresponding to $ φ_n $They are tight

I am aware of the test of a different version where convergence occurs in the entire real line. But what to do in this case?

differential equations – Non-autonomous ODE uses NDSolve, error: Step Size is effectively zero; The singularity or rigidity of the system is suspected.

I have seen this error NDSolve :: ndsz many times when I use NDSolve To obtain the solution of a non-autonomous ODE. I try but everything has failed. Thanks, Here is the code, very simple.

    s = NDSolve[{x'
Y
X[0] == 1, and[0] == 1}, {x