Consider the equation

$$\frac{d y}{d x}=1-y^{2} .$$

Using small line segments, sketch the flow directions in $x \geqslant 0,-2 \leqslant y \leqslant 2$ implied by the right-hand side of $(*)$. Find the general solution (i) in $|y|<1$, (ii) in $|y|>1$.

Sketch a solution curve in each of the three regions $y>1,|y|<1$, and $y<-1$.