Solved: Direction field analysis Consider the general
Chapter 7, Problem 69(choose chapter or problem)
Direction field analysis Consider the general first-order initial value problem y _1t2 = ay + b, y102 = y0, for t 0, where a, b, and y0 are real numbers. a. Explain why y = -b>a is an equilibrium solution and corresponds to horizontal line segments in the direction field. b. Draw a representative direction field in the case that a 7 0. Show that if y0 7 -b>a, then the solution increases for t 0 and if y0 6 -b>a, then the solution decreases for t 0. c. Draw a representative direction field in the case that a 6 0. Show that if y0 7 -b>a, then the solution decreases for t 0 and if y0 6 -b>a, then the solution increases for t 0.
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