Solution
= Solution
The initial point has $x_0=0$, so its orbit remains in $-1<x<1$. Integrating the orbit equation from part (iv) and using $y(0)=y_0$ gives
$$
\boxed{y(x)=y_0(1-x^2)^{k/2},\qquad -1<x<1.}
$$
This formula also covers $y_0=0$ and $k=0$ within the open strip. The endpoints are approached only as infinite time limits and have the behavior classified in part (iv).