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2. The functions ₁(t) = is given by: erot, 2(t) = terot give a fundamental set of solutions to the ODE y" - 2roy' + r²y = 0 (a) Calculate the Wronskian W[1,2] (t). (b) Find the function K(s, t) so that the solution to y" — 2roy' + r²y = g(t), y(0) = y'(0) = 0 *K(s, t)g(s)ds (Hint: see Theorem 3.6.1 from the textbook) (c) Find the solution to y" - 2roy' + r²y = |t|, y(0) = y'(0) = 0

2. The functions ₁(t) = is given by: erot, 2(t) = terot give a fundamental set of solutions to the ODE y" - 2roy' + r²y = 0 (a) Calculate the Wronskian W[1,2] (t). (b) Find the function K(s, t) so that the solution to y" — 2roy' + r²y = g(t), y(0) = y'(0) = 0 *K(s, t)g(s)ds (Hint: see Theorem 3.6.1 from the textbook) (c) Find the solution to y" - 2roy' + r²y = |t|, y(0) = y'(0) = 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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2. The functions ₁(t) = erot, ₂(t) = terot give a fundamental set of solutions to the ODE y" − 2roy' + r²y = 0 (a) Calculate the Wronskian W[1, 2] (t). (b) Find the function K(s, t) so that the solution to is given by: y" − 2roy' + r²y = g(t), _y(0) = y'(0) = 0 *K(s, t)g(s)ds 0 (Hint: see Theorem 3.6.1 from the textbook) (c) Find the solution to y" − 2roy' + r²y = |t|,_y(0) = y'(0) = 0
Transcribed Image Text:2. The functions ₁(t) = erot, ₂(t) = terot give a fundamental set of solutions to the ODE y" − 2roy' + r²y = 0 (a) Calculate the Wronskian W[1, 2] (t). (b) Find the function K(s, t) so that the solution to is given by: y" − 2roy' + r²y = g(t), _y(0) = y'(0) = 0 *K(s, t)g(s)ds 0 (Hint: see Theorem 3.6.1 from the textbook) (c) Find the solution to y" − 2roy' + r²y = |t|,_y(0) = y'(0) = 0
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