A general solution may fail to produce all solutions of a differential equation. In Exercise, show that y = 0 is a solution of the differential equation, but no value of C in the given general solution will produce this solution. In Exercise 6, show that the given solution is a general solution of the differential equation. Use a computer or calculator to sketch the solutions for the given values of the arbitrary constant. Experiment with different intervals for t until you have a plot that shows what you consider to be the most important behavior of the family. Exercise 6
y = )44 - y( = 4/(1 Ce- 4 t ), C = 1, 2,..., 5