7 1 1 Almost done! You know I (y) = ( ) + −1² ( , + 2) 2 2 transform of each term on the right side of this equation. L-1 7 GC)) = 2 1 1 +(-(+)) - 2 s+2 L -1 To find y(t), find the inverse Laplace
7 1 1 Almost done! You know I (y) = ( ) + −1² ( , + 2) 2 2 transform of each term on the right side of this equation. L-1 7 GC)) = 2 1 1 +(-(+)) - 2 s+2 L -1 To find y(t), find the inverse Laplace
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Homework 9: Question 1
Please help with the part 4
![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)
L(7)
=
=
=
L(y):
L(y)
You got it! You now have the equation
7
S
SL(y) - 3
2L (y)
7
S
sL(y) — 3+2L(y)
Use factoring and algebra to solve this equation for L(y). Leave any denominator(s) in factored
form.
L
Nice! You have shown that L(y)
side of this equation.
=
(7+3s)
(s(s+2))
7
1
= 2s 2(s+2)
7
L -1
- ((:)) -
1
Almost done! You know [(y)
77 ( ² ) + - 1²/ ( 0 ² 2 )
2
2
transform of each term on the right side of this equation.
1 1
+²^(-(-₂)).
2
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
Part 4 of 5
To find y(t), find the inverse Laplace](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9086a1c0-d376-4c80-871f-f484ad7b10c1%2F9c575959-7ffd-4d13-a885-4e320556f911%2F2qysss_processed.png&w=3840&q=75)
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)
L(7)
=
=
=
L(y):
L(y)
You got it! You now have the equation
7
S
SL(y) - 3
2L (y)
7
S
sL(y) — 3+2L(y)
Use factoring and algebra to solve this equation for L(y). Leave any denominator(s) in factored
form.
L
Nice! You have shown that L(y)
side of this equation.
=
(7+3s)
(s(s+2))
7
1
= 2s 2(s+2)
7
L -1
- ((:)) -
1
Almost done! You know [(y)
77 ( ² ) + - 1²/ ( 0 ² 2 )
2
2
transform of each term on the right side of this equation.
1 1
+²^(-(-₂)).
2
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
Part 4 of 5
To find y(t), find the inverse Laplace
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