3) Show that for any constants M, k, and a, the function k(t – a) y(t) M1+tanh 2 y' satisfies the logistic equation: = k(1 – ) y y M Note: The function tanh is the hyperbolic tangent e* - e-* e2x – 1 function: tanh x = ex + e-x e2x + 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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3) Show that for any constants M, k, and a, the
function
y(t)
1
M1+tanh
k(t – a)
2
y'
satisfies the logistic equation:
y
k(1 –
%).
y
M
Note: The function tanh is the hyperbolic tangent
ex – e-x
e2x – 1
-
function: tanh x =
ex + e-*
+ e-x
e2x + 1
Transcribed Image Text:3) Show that for any constants M, k, and a, the function y(t) 1 M1+tanh k(t – a) 2 y' satisfies the logistic equation: y k(1 – %). y M Note: The function tanh is the hyperbolic tangent ex – e-x e2x – 1 - function: tanh x = ex + e-* + e-x e2x + 1
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