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Solve the following equations using the Laplace transform. (a) y" - 2y' + 2y = et; y(0) = 0, y'(0) = 1 (b) y″ +2y' +5y = 0; y(0) = 2, y'(0) = −1 (c) y" + w²y = cos(2t), w² ₤4; y(0) = 1, y'(0) = 0 (d) y" + 4y { 1, 0 ≤t<л, О, π ≤t < ∞0; y(0) = 1, y'(0) = 0

Solve the following equations using the Laplace transform. (a) y" - 2y' + 2y = et; y(0) = 0, y'(0) = 1 (b) y″ +2y' +5y = 0; y(0) = 2, y'(0) = −1 (c) y" + w²y = cos(2t), w² ₤4; y(0) = 1, y'(0) = 0 (d) y" + 4y { 1, 0 ≤t<л, О, π ≤t < ∞0; y(0) = 1, 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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Solve the following equations using the Laplace transform. (a) y" - 2y' + 2y = et; y(0) = 0, y'(0) = 1 (b) y″ +2y' +5y = 0; y(0) = 2, y'(0) = −1 (c) y" + w²y = cos(2t), w² ₤4; y(0) = 1, y'(0) = 0 (d) y" + 4y { 1, 0 ≤t<л, О, π ≤t < ∞0; y(0) = 1, y'(0) = 0
Transcribed Image Text:Solve the following equations using the Laplace transform. (a) y" - 2y' + 2y = et; y(0) = 0, y'(0) = 1 (b) y″ +2y' +5y = 0; y(0) = 2, y'(0) = −1 (c) y" + w²y = cos(2t), w² ₤4; y(0) = 1, y'(0) = 0 (d) y" + 4y { 1, 0 ≤t<л, О, π ≤t < ∞0; y(0) = 1, y'(0) = 0
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