Chapter 9.2, Problem 19E

a.

To determine

To Find: The solution of the given differential equation that are constant for all $t\ge 0$

b.

To determine

To Find: The region where the solution is increasing or decreasing.

c.

To determine

To Find: The initial condition for $y\left(0\right)=A$ where the solution is increasing or decreasing.

d.

To determine

To sketch: The direction field of the given differential equation $y^{\prime }\left(t\right)=\cos y$.