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) = Pa
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) = Pa
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 help with the part 2
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) =
=
Part 2 of 3
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