Moderate# What Uniqueness Theorem Tells us About Initial Value Problem

DIFFEQ-GUIXGJ

Assuming that $0 < t_0 <1$, what does the existence and uniqueness theorem tell us about the initial value problem:

$$tx'+\frac{x}{1-t}=\sqrt{1-x^2},\ x(t_0)=x_0$$

Choose the **MOST** complete answer.