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Problem 4: Consider the initial value problem: y" + y – 2y = 0 , y(0) = 2 , y/(0) = 3 a For which value of B does the solution satisfy lim-+0 Y(t) = 0 ? b For which value(s) of B is the solution y(t) # 0 for all -0

Problem 4: Consider the initial value problem: y" + y – 2y = 0 , y(0) = 2 , y/(0) = 3 a For which value of B does the solution satisfy lim-+0 Y(t) = 0 ? b For which value(s) of B is the solution y(t) # 0 for all -0

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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Problem 4: Consider the initial value problem: y" + y – 2y = 0 , y(0) = 2 , y'(0) = ß a For which value of 3 does the solution satisfy lim;0 Y(t) = 0 ? b For which value(s) of ß is the solution y(t) # 0 for all -∞ <t < oo? That is, for which value(s) of B does the graph of the solution, y(t), never touch the t-axis?
Transcribed Image Text:Problem 4: Consider the initial value problem: y" + y – 2y = 0 , y(0) = 2 , y'(0) = ß a For which value of 3 does the solution satisfy lim;0 Y(t) = 0 ? b For which value(s) of ß is the solution y(t) # 0 for all -∞ <t < oo? That is, for which value(s) of B does the graph of the solution, y(t), never touch the t-axis?
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