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For any given ɛ > 0, find the unique solution yɛ (t) to the initial value oblem y” − 2y′ + (1 − ɛ²) y = 0, Define for any fixed t, g (t) = y (0) = 0, y′ (0) = 1. lim_yɛ (t). € →0+ aluate g (t) and verify that y = g(t) is a solution to the initial value oblem y" — 2y' + y = 0, y (0) = 0, y′ (0) = 1.

For any given ɛ > 0, find the unique solution yɛ (t) to the initial value oblem y” − 2y′ + (1 − ɛ²) y = 0, Define for any fixed t, g (t) = y (0) = 0, y′ (0) = 1. lim_yɛ (t). € →0+ aluate g (t) and verify that y = g(t) is a solution to the initial value oblem y" — 2y' + y = 0, y (0) = 0, y′ (0) = 1.

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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4. (a) For any given ɛ > 0, find the unique solution yɛ (t) to the initial value problem y" - 2y + (1-²) y = 0, (b) Define for any fixed t, g (t): = y (0) = 0, y' (0) = 1. lim_yɛ (t). ε→0+ Evaluate g (t) and verify that y = g (t) is a solution to the initial value problem y" - 2y + y = 0, y (0) = 0, y' (0) = 1.
Transcribed Image Text:4. (a) For any given ɛ > 0, find the unique solution yɛ (t) to the initial value problem y" - 2y + (1-²) y = 0, (b) Define for any fixed t, g (t): = y (0) = 0, y' (0) = 1. lim_yɛ (t). ε→0+ Evaluate g (t) and verify that y = g (t) is a solution to the initial value problem y" - 2y + y = 0, y (0) = 0, y' (0) = 1.
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