Chapter D1.2, Problem 19E

Increasing and decreasing solutions Consider the following differential equations. A detailed direction field is not needed.

a.    Find the solutions that are constant, for all t ≥ 0 (the equilibrium solutions).

b.    In what regions are solutions increasing? Decreasing?

c.    Which initial conditions y(0) = A lead to solutions that are increasing in time? Decreasing?

d.    Sketch the direction field and verify that it is consistent with parts (a)–(c).

19.    y′(t) = cos y, for |y| ≤ π