Chapter 9.2, Problem 1E

A direction field for the differential equation $y^{\prime }=x\cos \pi y$ is shown.

(a) Sketch the graphs of the solutions that satisfy the given initial conditions.

(i) $y\left(0\right)=0$

(ii) $y\left(0\right)=0.5$

(iii) $y\left(0\right)=1$

(iv) $y\left(0\right)=1.6$

(b) Find all the equilibrium solutions.