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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.8 - Problem 61ae
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.8 - Problem 61ae

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# Direction field analysis Consider the general first-order

ISBN: 9780321570567 2

## Solution for problem 61AE Chapter 7.8

Calculus: Early Transcendentals | 1st Edition

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Problem 61AE

Direction field analysis Consider the general first-order initial value problem $$y^{\prime}(t)=a y+b$$, $$y(0)=y_{0}$$, for $$t \geq 0$$, where a, b, and v0 are real numbers.

a. Explain why y = -b/a is an equilibrium solution and corresponds to a horizontal line in the direction field.

b. Draw a representative direction field in the case that a > 0. Show that if $$y_{0}>-b / a$$, then the solution increases for $$t \geq 0$$, and if $$y_{0}<-b / a$$, then the solution decreases for $$t \geq 0$$.

c. Draw a representative direction field in the case that a > 0. Show that if $$y_{0}>-b / a$$, then the solution decreases for $$t \geq 0$$, and if $$y_{0}<-b / a$$, then the solution increases for $$t \geq 0$$.

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