Concept explainers
Direction field analysis Consider the first-order initial value problem
a. Explain why y = –b/a is an solution and corresponds to a horizontal line in the direction field.
b. Draw a representative direction fields in the case that a > 0. Show that if A > –b/a, then the solution increases for t ≥ 0 and if A < –b/a, then the solution decreases for t ≥ 0
c. Draw a representative direction fields in the case that a < 0. Show that if A > –b/a, then the solution decreases for t ≥ 0 and if A < –b/a, then the solution increases for t ≥ 0
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