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3) Show that for any constants M, k, and a, the function k(t – a) y(t) : -M1+ tanh = 2 2 у satisfies the logistic equation: = k y M e2x Note: The function tanh is the hyperbolic tangent function : tanh x = et — е 1 ex + e-x е2х +

3) Show that for any constants M, k, and a, the function k(t – a) y(t) : -M1+ tanh = 2 2 у satisfies the logistic equation: = k y M e2x Note: The function tanh is the hyperbolic tangent function : tanh x = et — е 1 ex + e-x е2х +

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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3) Show that for any constants M, k, and a, the function (놀의)) 1 - M1+ tanh k(t – a) - y(t) = 2 y satisfies the logistic equation: y = (1 - ) y e* – e-x e2x 1 Note: The function tanh is the hyperbolic tangent function 2 : tanh x = ex + e-x e2x + 1
Transcribed Image Text:3) Show that for any constants M, k, and a, the function (놀의)) 1 - M1+ tanh k(t – a) - y(t) = 2 y satisfies the logistic equation: y = (1 - ) y e* – e-x e2x 1 Note: The function tanh is the hyperbolic tangent function 2 : tanh x = ex + e-x e2x + 1
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