Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 1 / 31E / v / 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 $y(0)=y_0$ givesThis 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).