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Problem 1: Answer each of the following questions. (a) Give the candidate general solution using the proposed solution sets for the second-order differential equation y"(t) + pı (t)y'(t) + P2(t)y(t) = 0. (i) yı (t) = exp(-3t), y2(t) = texp(-3t) y(t) = (ii) yı(t) = exp(-t) cos(2t), y2(t) = exp(-t) sin(2t) y(t) = (iii) y1(t) = t exp(-t), y2(t) = exp(-t) y(t): (b) Compute the Wronskian W(t) for each of the proposed solution sets in problem (a) for general t e (-1, 1) and at to = 0. State if the set forms a fundamental solution set or not. (i) W (t) = W (to) = Fundamental solution set?

Problem 1: Answer each of the following questions. (a) Give the candidate general solution using the proposed solution sets for the second-order differential equation y"(t) + pı (t)y'(t) + P2(t)y(t) = 0. (i) yı (t) = exp(-3t), y2(t) = texp(-3t) y(t) = (ii) yı(t) = exp(-t) cos(2t), y2(t) = exp(-t) sin(2t) y(t) = (iii) y1(t) = t exp(-t), y2(t) = exp(-t) y(t): (b) Compute the Wronskian W(t) for each of the proposed solution sets in problem (a) for general t e (-1, 1) and at to = 0. State if the set forms a fundamental solution set or not. (i) W (t) = W (to) = Fundamental solution set?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Problem 1: Answer each of the following questions. (a) Give the candidate general solution using the proposed solution sets for the second-order differential equation y"(t) + pı (t)y'(t) + P2(t)y(t) = 0. (i) yı (t) = exp(-3t), y2(t) = texp(-3t) y(t) = (ii) yı(t) = exp(-t) cos(2t), y2(t) = exp(-t) sin(2t) y(t) = (iii) y1(t) = t exp(-t), y2(t) = exp(-t) y(t): (b) Compute the Wronskian W(t) for each of the proposed solution sets in problem (a) for general t e (-1, 1) and at to = 0. State if the set forms a fundamental solution set or not. (i) W (t) = W (to) = Fundamental solution set? (ii) W (t) = W (to) = Fundamental solution set? (ii) W (t) = W (to) = Fundamental solution set?
Transcribed Image Text:Problem 1: Answer each of the following questions. (a) Give the candidate general solution using the proposed solution sets for the second-order differential equation y"(t) + pı (t)y'(t) + P2(t)y(t) = 0. (i) yı (t) = exp(-3t), y2(t) = texp(-3t) y(t) = (ii) yı(t) = exp(-t) cos(2t), y2(t) = exp(-t) sin(2t) y(t) = (iii) y1(t) = t exp(-t), y2(t) = exp(-t) y(t): (b) Compute the Wronskian W(t) for each of the proposed solution sets in problem (a) for general t e (-1, 1) and at to = 0. State if the set forms a fundamental solution set or not. (i) W (t) = W (to) = Fundamental solution set? (ii) W (t) = W (to) = Fundamental solution set? (ii) W (t) = W (to) = Fundamental solution set?
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