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2. Let c be a positive number. A differential equation of the form = ky¹+e, where k is a positive constant, is called a doomsday equation because the exponent in the expression ky¹+c is larger than the exponent 1 for natural growth. a) Determine the solution that satisfies the initial condition y(0) = yo. b) Show that there is a finite time t = T (doomsday) such that lim→T- y(t): = ∞. c) An especially prolific breed of rabbits has the growth term ky¹.01. If two such rabbits breed initially and the warren has 16 rabbits after three months, then when is doomsday?

2. Let c be a positive number. A differential equation of the form = ky¹+e, where k is a positive constant, is called a doomsday equation because the exponent in the expression ky¹+c is larger than the exponent 1 for natural growth. a) Determine the solution that satisfies the initial condition y(0) = yo. b) Show that there is a finite time t = T (doomsday) such that lim→T- y(t): = ∞. c) An especially prolific breed of rabbits has the growth term ky¹.01. If two such rabbits breed initially and the warren has 16 rabbits after three months, then when is doomsday?

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 dt 2. Let c be a positive number. A differential equation of the form d = ky¹+e, where k is a positive constant, is called a doomsday equation because the exponent in the expression ky¹+c is larger than the exponent 1 for natural growth. a) Determine the solution that satisfies the initial condition y(0) = yo. b) Show that there is a finite time t = T (doomsday) such that lim T-y(t) = ∞. c) An especially prolific breed of rabbits has the growth term ky1.01. If two such rabbits breed initially and the warren has 16 rabbits after three months, then when is doomsday?
Transcribed Image Text:dy dt 2. Let c be a positive number. A differential equation of the form d = ky¹+e, where k is a positive constant, is called a doomsday equation because the exponent in the expression ky¹+c is larger than the exponent 1 for natural growth. a) Determine the solution that satisfies the initial condition y(0) = yo. b) Show that there is a finite time t = T (doomsday) such that lim T-y(t) = ∞. c) An especially prolific breed of rabbits has the growth term ky1.01. If two such rabbits breed initially and the warren has 16 rabbits after three months, then when is doomsday?
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