6) Consider the initial value problem y + cos πι + e²бty = 0, y(-1) = 0, y' (-1) = 0 Which of these statements are true? Select all that apply. A) There exists a nonzero real number r such that y(t) = ert is a solution of the initial value problem. B) The constant function y(t) = -1 is a solution of this initial value problem for all real numbers t. C) The constant function y(t) = 0 is the unique solution of this initial value problem on the interval (-∞, ∞). D) This initial value problem has only one solution on the interval (-7, 5). E) There must exist a function y = q(t) that satisfies this initial value problem on the interval (-7,∞).
6) Consider the initial value problem y + cos πι + e²бty = 0, y(-1) = 0, y' (-1) = 0 Which of these statements are true? Select all that apply. A) There exists a nonzero real number r such that y(t) = ert is a solution of the initial value problem. B) The constant function y(t) = -1 is a solution of this initial value problem for all real numbers t. C) The constant function y(t) = 0 is the unique solution of this initial value problem on the interval (-∞, ∞). D) This initial value problem has only one solution on the interval (-7, 5). E) There must exist a function y = q(t) that satisfies this initial value problem on the interval (-7,∞).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:6) Consider the initial value problem
y + cos
πι
+ e²бty = 0, y(-1) = 0, y' (-1) = 0
Which of these statements are true? Select all that apply.
A) There exists a nonzero real number r such that y(t) = ert is a solution of the initial value
problem.
B) The constant function y(t) = -1 is a solution of this initial value problem for all real numbers
t.
C) The constant function y(t) = 0 is the unique solution of this initial value problem on the
interval (-∞, ∞).
D) This initial value problem has only one solution on the interval (-7, 5).
E) There must exist a function y = q(t) that satisfies this initial value problem on the interval
(-7,∞).
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