Adifferential equation of the form y prime (t )equalsf(y) is said to be autonomous (the function f depends only on y). the constant function yequals y 0 is an equilibrium solution of the equation provided upper f (y 0 )equals0 (because then y prime (t )equals0, and the solution remains constant for all t). note that equilibrium solutions correspond to horizontal line segments in the direction field. note also that for autonomous equations, the direction field is independent of t. consider the equation y prime (t )equals3 sine y .

a. find all equilibrium solutions in the interva