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Question 2. Let c be a positive number. A differential equation of the form dy dt = ky¹+c = 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. = yo. (a) Determine the solution that satisfies the initial condition y(0) (b) Show that there is a finite time t = T (doomsday) such that lim T-y(t) = ∞.

Question 2. Let c be a positive number. A differential equation of the form dy dt = ky¹+c = 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. = yo. (a) Determine the solution that satisfies the initial condition y(0) (b) Show that there is a finite time t = T (doomsday) such that lim T-y(t) = ∞.

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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Question 2. Let c be a positive number. A differential equation of the form dy dt = ky¹+ = 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) = ∞.
Transcribed Image Text:Question 2. Let c be a positive number. A differential equation of the form dy dt = ky¹+ = 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) = ∞.
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