y = ay (1 -) where a, k > 0 are real constants. (a) Note that the logistic growth equation is separable. Use separation of variables to solve the logistic growth equation when a = 2.8 and k = 10. That is, solve the separable equation: / = 2.8y (1- ) 10. State your solution explicitly. (b) Note that the logistic growth equation is also a Bernoulli equation: y' – ay = - Solve the logistic equation from (a) as a Bernoulli equation. State your solution explicitly. (c) Write 1-2 sentences comparing your work for parts (a)-(b). Are your answers consistent? Did you find one method easier than the other?

y = ay (1 -) where a, k > 0 are real constants. (a) Note that the logistic growth equation is separable. Use separation of variables to solve the logistic growth equation when a = 2.8 and k = 10. That is, solve the separable equation: / = 2.8y (1- ) 10. State your solution explicitly. (b) Note that the logistic growth equation is also a Bernoulli equation: y' – ay = - Solve the logistic equation from (a) as a Bernoulli equation. State your solution explicitly. (c) Write 1-2 sentences comparing your work for parts (a)-(b). Are your answers consistent? Did you find one method easier than the other?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

/ = ay (1-)
where a, k > 0 are real constants.
(a) Note that the logistic growth equation is separable. Use separation of variables to solve the logistic
growth equation when a = 2.8 and k = 10. That is, solve the separable equation:
y' = 2.8y (1–
10
State your solution explicitly.
(b) Note that the logistic growth equation is also a Bernoulli equation:
y' – ay = -
y?
Solve the logistic equation from (a) as a Bernoulli equation. State your solution explicitly.
(c) Write 1-2 sentences comparing your work for parts (a)-(b). Are your answers consistent? Did you
find one method easier than the other?

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