Nice! You have shown that L(y) side of this equation. L(y) = = 7+3s s(s+2) Find the partial fraction decomposition of the right

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 1

Please help with part 3

After part 3, Find the partial fraction decomposition of the right side of this equation.

L(y) = ______

 

 

In this exercise you will use Laplace transforms to solve the differential equation
y'+2y = 7, y(0) = 3.
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')
L(2y) = 2L(y)
L(7):
L(y)
=
=
L(y)
sL(y) – 3
7
S
You got it! You now have the equation
7
sL(y) — 3 + 2L(y)
S
Use factoring and algebra to solve this equation for L(y). Leave any denominator(s) in factored
form.
=
Nice! You have shown that L(y)
side of this equation.
(7+3s)
(s(s+2))
=
Part 1 of 5
7+ 3s
s(s+ 2)
Part 2 of 5
Part 3 of 5
Find the partial fraction decomposition of the right
Transcribed Image Text:In this exercise you will use Laplace transforms to solve the differential equation y'+2y = 7, y(0) = 3. 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') L(2y) = 2L(y) L(7): L(y) = = L(y) sL(y) – 3 7 S You got it! You now have the equation 7 sL(y) — 3 + 2L(y) S Use factoring and algebra to solve this equation for L(y). Leave any denominator(s) in factored form. = Nice! You have shown that L(y) side of this equation. (7+3s) (s(s+2)) = Part 1 of 5 7+ 3s s(s+ 2) Part 2 of 5 Part 3 of 5 Find the partial fraction decomposition of the right
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