In this exercise you will use Laplace transforms to solve the differential equation y"+5y'+6y= 0, y(0) = 1, 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) - s L(5y') = 5(sL(y)-1) L(6y) L(0) = L(y) = 6L (y) = 0 Great! You now have the equation s²L(y) — s +5sL(y) − 5 + 6L(y) = 0. Use factoring and algebra to solve this equation for L(y). Leave any denominator(s) in factored form. = Part 2 of 5
In this exercise you will use Laplace transforms to solve the differential equation y"+5y'+6y= 0, y(0) = 1, 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) - s L(5y') = 5(sL(y)-1) L(6y) L(0) = L(y) = 6L (y) = 0 Great! You now have the equation s²L(y) — s +5sL(y) − 5 + 6L(y) = 0. Use factoring and algebra to solve this equation for L(y). Leave any denominator(s) in factored form. = Part 2 of 5
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 5
Please help with part 2
Transcribed Image Text:In this exercise you will use Laplace transforms to solve the differential equation
y"+5y+6y= 0, y(0) = 1, 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) - s
L(5y') = 5(sL(y) – 1)
L(6y) = 6L (y)
L(0)
= 0
L(y)
Great! You now have the equation
s²L(y) — s +5sL(y) − 5 + 6L(y) = 0 .
Use factoring and algebra to solve this equation for L(y). Leave any denominator(s) in factored
form.
Part 2 of 5
=
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