Entry and Exit through boundaries

Consider the following one dimensional SDE.
dX_t&= \cos( X_t )^\alpha dW(t)\\
Consider the equation for \(\alpha >0\). On what interval do you expect to find the solution at all times ? Classify the behavior at the boundaries.

For what values of \(\alpha < 0\) does it seem reasonable to define the process ? any ? justify your answer.

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