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=y-2y³, y(0) = 1. dt get to translate back to the desi

=y-2y³, y(0) = 1. dt get to translate back to the desi

Advanced Engineering Mathematics
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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dy 16. We have seen that Bernoulli's change of variable z(t) = 1/y(t) transforms the nonlinear logistic equation ay-by² into a linear equation. There is a more general version of this change of variables. Consider the equation dt dy dt =ay - by", where n is any (positive or negative) integer, and a, b are constants. Let z(t) = y(t)¹-", and find the equation satisfied by z. This equation should be linear. Use this change of variables to solve the initial value problem dy =y - 2y³, dt (After you find z(t), don't forget to translate back to the desired solution y(t).) y(0)= = 1.
Transcribed Image Text:dy 16. We have seen that Bernoulli's change of variable z(t) = 1/y(t) transforms the nonlinear logistic equation ay-by² into a linear equation. There is a more general version of this change of variables. Consider the equation dt dy dt =ay - by", where n is any (positive or negative) integer, and a, b are constants. Let z(t) = y(t)¹-", and find the equation satisfied by z. This equation should be linear. Use this change of variables to solve the initial value problem dy =y - 2y³, dt (After you find z(t), don't forget to translate back to the desired solution y(t).) y(0)= = 1.
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