3) Show that for any constants M, k, and a, the function (",) A(1 - ) y(t) 1 ·M|1+tanh ´k(t – a) satisfies the logistic equation: M

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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3) Show that for any constants M, k, and a, the function
y(t)
1
M|1+tanh
´k(t
а)
= k(1-
satisfies the logistic equation:
M
1
Note: The function tanh is the hyperbolic tangent function 2: tanh x
e
2a +1
||
Transcribed Image Text:3) Show that for any constants M, k, and a, the function y(t) 1 M|1+tanh ´k(t а) = k(1- satisfies the logistic equation: M 1 Note: The function tanh is the hyperbolic tangent function 2: tanh x e 2a +1 ||
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