Let Solve the differential equation using Laplace transforms. y(t) = g(t) = { t if t≤2π 2π if t>2π y" + 16y= g(t), y(0) = 5, y(0) = 5 ift ≤2x ift > 2π function f(t) 1 tn eat sin at cos at sinh at cosh at e-at f(t) U(ta) or Ua(t) (a ≥ 0) (ta) (a> 0) U(t − a)f(t − a) or Ua(t)f(t − a) f(n)(t) (−t)" f (t) - (fg)(t) = f(r)g(t − T) dr Laplace transform F(s) 1/s (s > 0) n!/sn+1 (s > 0) 1/(s – a) (s> a) a/(s²+a²) (s > 0) s/(s² + a²) (s > 0) a/(s² - a²) (s> |a|) s/(s² – a²) F(s+a (s>|a|) -as e S S 0) as e as e S F(s F(n)(s) F(s)G(s) sn ¯¹ƒ (0) — sn−² ƒ'(0) … … … — ƒ (n−¹) (0)
Let Solve the differential equation using Laplace transforms. y(t) = g(t) = { t if t≤2π 2π if t>2π y" + 16y= g(t), y(0) = 5, y(0) = 5 ift ≤2x ift > 2π function f(t) 1 tn eat sin at cos at sinh at cosh at e-at f(t) U(ta) or Ua(t) (a ≥ 0) (ta) (a> 0) U(t − a)f(t − a) or Ua(t)f(t − a) f(n)(t) (−t)" f (t) - (fg)(t) = f(r)g(t − T) dr Laplace transform F(s) 1/s (s > 0) n!/sn+1 (s > 0) 1/(s – a) (s> a) a/(s²+a²) (s > 0) s/(s² + a²) (s > 0) a/(s² - a²) (s> |a|) s/(s² – a²) F(s+a (s>|a|) -as e S S 0) as e as e S F(s F(n)(s) F(s)G(s) sn ¯¹ƒ (0) — sn−² ƒ'(0) … … … — ƒ (n−¹) (0)
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
![Let
Solve the differential equation
using Laplace transforms.
y(t) =
g(t) = {
t
if t≤2π
2π if t>2π
y" + 16y= g(t),
y(0) = 5, y(0) = 5
ift ≤2x
ift > 2π](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2c11aba0-fb13-42a3-9a96-39222fc0cebd%2F97ea431b-4cc2-4f4e-9101-d2e0330e0d61%2Fweqt2kp_processed.png&w=3840&q=75)
Transcribed Image Text:Let
Solve the differential equation
using Laplace transforms.
y(t) =
g(t) = {
t
if t≤2π
2π if t>2π
y" + 16y= g(t),
y(0) = 5, y(0) = 5
ift ≤2x
ift > 2π
![function f(t)
1
tn
eat
sin at
cos at
sinh at
cosh at
e-at f(t)
U(ta) or Ua(t) (a ≥ 0)
(ta) (a> 0)
U(t − a)f(t − a) or Ua(t)f(t − a)
f(n)(t)
(−t)" f (t)
-
(fg)(t) = f(r)g(t − T) dr
Laplace transform F(s)
1/s
(s > 0)
n!/sn+1 (s > 0)
1/(s – a)
(s> a)
a/(s²+a²) (s > 0)
s/(s² + a²)
(s > 0)
a/(s² - a²)
(s> |a|)
s/(s² – a²)
F(s+a
(s>|a|)
-as
e
S S
0)
as
e
as
e
S
F(s
F(n)(s)
F(s)G(s)
sn
¯¹ƒ (0) — sn−² ƒ'(0) … … … — ƒ (n−¹) (0)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2c11aba0-fb13-42a3-9a96-39222fc0cebd%2F97ea431b-4cc2-4f4e-9101-d2e0330e0d61%2Fe87jkmg_processed.png&w=3840&q=75)
Transcribed Image Text:function f(t)
1
tn
eat
sin at
cos at
sinh at
cosh at
e-at f(t)
U(ta) or Ua(t) (a ≥ 0)
(ta) (a> 0)
U(t − a)f(t − a) or Ua(t)f(t − a)
f(n)(t)
(−t)" f (t)
-
(fg)(t) = f(r)g(t − T) dr
Laplace transform F(s)
1/s
(s > 0)
n!/sn+1 (s > 0)
1/(s – a)
(s> a)
a/(s²+a²) (s > 0)
s/(s² + a²)
(s > 0)
a/(s² - a²)
(s> |a|)
s/(s² – a²)
F(s+a
(s>|a|)
-as
e
S S
0)
as
e
as
e
S
F(s
F(n)(s)
F(s)G(s)
sn
¯¹ƒ (0) — sn−² ƒ'(0) … … … — ƒ (n−¹) (0)
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)