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Ex2: Solve by using Laplace transform y'-x = et • x'+y = e=t, where, x = 0, y = 0,

Ex2: Solve by using Laplace transform y'-x = et • x'+y = e=t, where, x = 0, y = 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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Ex2: Solve by using Laplace transform • y'-x = et x'+y = e-t, where, x = 0, y = 0, • Sol: 1) Express both equations in L.T, • [sy(s) – y(0)] – x(s) • [sx(s) – x(0)] + y(s) = s-1 1 s+1 2) Insert the initial conditions, • sy(s) – x(s) = • sx(s) + y(s) : (1) s-1 1 (2) s+1
Transcribed Image Text:Ex2: Solve by using Laplace transform • y'-x = et x'+y = e-t, where, x = 0, y = 0, • Sol: 1) Express both equations in L.T, • [sy(s) – y(0)] – x(s) • [sx(s) – x(0)] + y(s) = s-1 1 s+1 2) Insert the initial conditions, • sy(s) – x(s) = • sx(s) + y(s) : (1) s-1 1 (2) s+1
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