(a) A direction field for the differential equation y9 − ys y 2 2ds y 2 4d is shown. Sketch the graphs of the solutions that satisfy the given initial conditions.

(i) ys0d − 20.3 (ii) ys0d − 1

(iii) ys0d − 3 (iv) ys0d − 4.3

(b) If the initial condition is ys0d −

c, for what values of c is limt l ` ystd finite? What are the equilibrium solutions?

Transcribed Image Text:

2 \///// / /////\ 2 ' ---- ---- 1----- y