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3s s² +4 Part 3 Well done! You have shown that L(y) To find y(t), find the inverse Laplace transform of the right side of this equation. If needed, use partial fractions. y(t) = .

3s s² +4 Part 3 Well done! You have shown that L(y) To find y(t), find the inverse Laplace transform of the right side of this equation. If needed, use partial fractions. y(t) = .

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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Homework 9: Question 3

Please answer part 3

In this exercise you will use Laplace transforms to solve the differential equation y"+4y= 0, y(0) = 3, y′(0) = 0. Find the Laplace transform of each term in the equation. Your answer(s) may contain L(y). Incorporate any initial conditions if necessary. L(y') = s²L(y) - 3s L(4y) = 4L(y) L(0) = = 0 You got it! You now have the equation s²L(y) — 3s + 4L(y) = 0 . Use factoring and algebra to solve this equation for L(y). L(y) = Well done! You have shown that L(y) 3s (²+4) y(t) = = = 3s s² + 4 Part 1 of 3 Part 2 of 3 To find y(t), find the inverse Laplace transform of the right side of this equation. If needed, use partial fractions. Part 3 of 3
Transcribed Image Text:In this exercise you will use Laplace transforms to solve the differential equation y"+4y= 0, y(0) = 3, y′(0) = 0. Find the Laplace transform of each term in the equation. Your answer(s) may contain L(y). Incorporate any initial conditions if necessary. L(y') = s²L(y) - 3s L(4y) = 4L(y) L(0) = = 0 You got it! You now have the equation s²L(y) — 3s + 4L(y) = 0 . Use factoring and algebra to solve this equation for L(y). L(y) = Well done! You have shown that L(y) 3s (²+4) y(t) = = = 3s s² + 4 Part 1 of 3 Part 2 of 3 To find y(t), find the inverse Laplace transform of the right side of this equation. If needed, use partial fractions. Part 3 of 3
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