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In numbers 1 and 2, solve the given IVP using Laplace transforms and the following substitutions. Given: L{x"} = s² - x(s) — x(0) - s — x'(0) L{x'} = $ - x(s) — x(0) - L{x} = x(s) 1. Solve x" + 4x' + 3x = 0 2. Solve x" + 8x' +16x = 7e-4t x(0) = 0, x'(0) = 2 x(0) = 0, x'(0) = 0

In numbers 1 and 2, solve the given IVP using Laplace transforms and the following substitutions. Given: L{x"} = s² - x(s) — x(0) - s — x'(0) L{x'} = $ - x(s) — x(0) - L{x} = x(s) 1. Solve x" + 4x' + 3x = 0 2. Solve x" + 8x' +16x = 7e-4t x(0) = 0, x'(0) = 2 x(0) = 0, x'(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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In numbers 1 and 2, solve the given IVP using Laplace transforms and the following substitutions. Given: L{x"} = s² - x(s) — x(0) - s — x'(0) - L{x'} = $•x(s) — x(0) L{x} = x(s) 1. Solve x" + 4x' + 3x = 0 2. Solve x" + 8x' + 16x= -4t = 7e-4 x(0) = 0, x'(0) = 2 x(0) = 0, x'(0) = 0
Transcribed Image Text:In numbers 1 and 2, solve the given IVP using Laplace transforms and the following substitutions. Given: L{x"} = s² - x(s) — x(0) - s — x'(0) - L{x'} = $•x(s) — x(0) L{x} = x(s) 1. Solve x" + 4x' + 3x = 0 2. Solve x" + 8x' + 16x= -4t = 7e-4 x(0) = 0, x'(0) = 2 x(0) = 0, x'(0) = 0
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