In this exercise you will use Laplace transforms to solve the differential equation y"+25y = 0, y(0) = 0, y′(0) = 6. 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) - 6 L(25y) 25L (y) L(0) L(y) = = 0 Good job! You now have the equation s²L(y) — 6 + 25L(y) = 0. Use factoring and algebra to solve this equation for L(y). = 6 +25 ▼ 6 s² + 25 ▼ Part 1 of 3 Part 2 of 3 Part 3 of 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) =
In this exercise you will use Laplace transforms to solve the differential equation y"+25y = 0, y(0) = 0, y′(0) = 6. 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) - 6 L(25y) 25L (y) L(0) L(y) = = 0 Good job! You now have the equation s²L(y) — 6 + 25L(y) = 0. Use factoring and algebra to solve this equation for L(y). = 6 +25 ▼ 6 s² + 25 ▼ Part 1 of 3 Part 2 of 3 Part 3 of 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
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 4
Please answer part 3
Transcribed Image Text:In this exercise you will use Laplace transforms to solve the differential equation
y"+25y = 0, y(0) = 0, y'(0) = 6.
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) - 6
25L (y)
=
L(25y):
L(0) = 0
L(y) =
Good job! You now have the equation
s²L(y) — 6 + 25L(y) = 0.
Use factoring and algebra to solve this equation for L(y).
=
=
6
2
S + 25
▼ Part 1 of 3
6
s² + 25
▼
Part 2 of 3
Part 3 of 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) =
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