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In Problems 3 through 8, you can use the solution formula for = ay+q(t): dt Find the solution y(t): dy dt 3. y - 3, y(0) = 2. +fe 0 y(t) = y(0)eat + eat e-as ¹8 q(s) ds.

In Problems 3 through 8, you can use the solution formula for = ay+q(t): dt Find the solution y(t): dy dt 3. y - 3, y(0) = 2. +fe 0 y(t) = y(0)eat + eat e-as ¹8 q(s) ds.

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter13: Conic Sections
Section13.1: Circles
Problem 48PS
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dy In Problems 3 through 8, you can use the solution formula for dt Find the solution y(t): dy dt 3. 4. 5. 6. dy dt dy dt dy dt = y − 3, y(0) = 2. = : 3y + 2e¯t, y(0) = 2. 2y+3e²t, y(0) = 1. -y + e-t cos(t), y(0) = 2. = y(t) = y(0)eat + eª at t L'e е ¹8 q(s) ds. -as = = ay + q(t): 7. Radium-223 has a half-life of 11.4 days. Find the decay rate a. Starting with a sample of 100 kg, how long will it take until only 20 kg are left? 8. Consider a population of bacteria with a growth rate of a = = 2. Assume that bacteria are harvested at a constant rate of 3 individuals per unit time. Find the general solution y(t) (leaving the initial population y(0) as a free parameter). Sketch a graph of the solution for a few different choices of y(0). Does this equation have any steady states?
Transcribed Image Text:dy In Problems 3 through 8, you can use the solution formula for dt Find the solution y(t): dy dt 3. 4. 5. 6. dy dt dy dt dy dt = y − 3, y(0) = 2. = : 3y + 2e¯t, y(0) = 2. 2y+3e²t, y(0) = 1. -y + e-t cos(t), y(0) = 2. = y(t) = y(0)eat + eª at t L'e е ¹8 q(s) ds. -as = = ay + q(t): 7. Radium-223 has a half-life of 11.4 days. Find the decay rate a. Starting with a sample of 100 kg, how long will it take until only 20 kg are left? 8. Consider a population of bacteria with a growth rate of a = = 2. Assume that bacteria are harvested at a constant rate of 3 individuals per unit time. Find the general solution y(t) (leaving the initial population y(0) as a free parameter). Sketch a graph of the solution for a few different choices of y(0). Does this equation have any steady states?
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