Question 12 Use Laplace Transforms to solve the initial value problem [y'+2y=f(x),y(0)=0] where a) O y(x)= b) O y(x)= c) O y(x)=- d) O y(x)=- f(x) = 4 2 -2 e ²x + 2 -2x -2 e ²x +1+e5-2x -2 e 0≤x and x < 3 3 ≤x 2e-²x - 2 2 e ²x+1+e6-2x 2e-2x - 2 -2 e ²x +1-3e6-2x -2 e 0≤x and x <3 3 ≤x 0≤x and x < 3 3 ≤x 0≤x and x < 3 3 ≤x -2e-²x - 2 0≤x and x <3 e-2x+1-3e6-2x 3 ≤ x
Question 12 Use Laplace Transforms to solve the initial value problem [y'+2y=f(x),y(0)=0] where a) O y(x)= b) O y(x)= c) O y(x)=- d) O y(x)=- f(x) = 4 2 -2 e ²x + 2 -2x -2 e ²x +1+e5-2x -2 e 0≤x and x < 3 3 ≤x 2e-²x - 2 2 e ²x+1+e6-2x 2e-2x - 2 -2 e ²x +1-3e6-2x -2 e 0≤x and x <3 3 ≤x 0≤x and x < 3 3 ≤x 0≤x and x < 3 3 ≤x -2e-²x - 2 0≤x and x <3 e-2x+1-3e6-2x 3 ≤ x
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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![Question 12
Use Laplace Transforms to solve the initial value problem
[y'+2y=f(x),y(0)=0]
where
a) O y(x)=
b) O y(x)=
c) O y(x)=-
d) O y(x)=-
f(x) =
4
2
-2 e ²x + 2
-2x
-2 e ²x +1+e5-2x
-2 e
0≤x and x < 3
3 ≤x
2e-²x - 2
2 e ²x+1+e6-2x
2e-2x - 2
-2 e ²x +1-3e6-2x
-2 e
0≤x and x <3
3 ≤x
0≤x and x < 3
3 ≤x
0≤x and x < 3
3 ≤x
-2e-²x - 2 0≤x and x <3
e-2x+1-3e6-2x
3 ≤ x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7533f7e4-73c2-4076-bfc2-24d84c7a3cfb%2Fa304c1ec-5392-4972-a211-89b163549371%2Fky23g6_processed.png&w=3840&q=75)
Transcribed Image Text:Question 12
Use Laplace Transforms to solve the initial value problem
[y'+2y=f(x),y(0)=0]
where
a) O y(x)=
b) O y(x)=
c) O y(x)=-
d) O y(x)=-
f(x) =
4
2
-2 e ²x + 2
-2x
-2 e ²x +1+e5-2x
-2 e
0≤x and x < 3
3 ≤x
2e-²x - 2
2 e ²x+1+e6-2x
2e-2x - 2
-2 e ²x +1-3e6-2x
-2 e
0≤x and x <3
3 ≤x
0≤x and x < 3
3 ≤x
0≤x and x < 3
3 ≤x
-2e-²x - 2 0≤x and x <3
e-2x+1-3e6-2x
3 ≤ x
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