3. y" + y' + 0.25y = 0, y(0) = 3, y'(0) = -3.5
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
Answer number 3
Please write legibly
Show complete solution
![Solve the following initial value problem and present its particular solution:
1. y" + y' + 9.25y = 0,
y(0) = 2,
y'(0) = 8
2. y" + y' – 2y = 0,
y(0) = -4,
y'(0) = -5
%3D
3. y" + y' + 0.25y = 0,
y(0) = 3,
y'(0) = -3.5
%3D
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48948c4f-5245-4e6c-91ab-abc15c3ebe25%2F78949638-42b4-44ba-a84f-eab4cd3b9327%2Fi6891ie_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Solve the following initial value problem and present its particular solution:
1. y" + y' + 9.25y = 0,
y(0) = 2,
y'(0) = 8
2. y" + y' – 2y = 0,
y(0) = -4,
y'(0) = -5
%3D
3. y" + y' + 0.25y = 0,
y(0) = 3,
y'(0) = -3.5
%3D
%3D
![(2²+a2 + b) = 0
The solution to the ODE depends on the nature of the
roots of the characteristic equation
EULER IDENTITIES
ea+ib
o FOR DIS TRcseR FUS
d=4=2 SHARE.
= e"(cos b + i sin b)
%3D
1
cos y =(e'y + e-iy)
sin y = (ety – e-ly)
Two Distinct Real Roots
1
Real Double Root
2i
1
y = cze21*+ c2xe?2*
5(e +e-Y)
cosh y =
2
1
Complex Conjugate Roots 11 = a + ib 12 = a – ib
sinh y =(ey – e-")
ey = cosh y + i sinh y
e-y = cosh y - i sinh y
y = eax(C1 cos bx + c2 sin bx)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48948c4f-5245-4e6c-91ab-abc15c3ebe25%2F78949638-42b4-44ba-a84f-eab4cd3b9327%2Fd7a14f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(2²+a2 + b) = 0
The solution to the ODE depends on the nature of the
roots of the characteristic equation
EULER IDENTITIES
ea+ib
o FOR DIS TRcseR FUS
d=4=2 SHARE.
= e"(cos b + i sin b)
%3D
1
cos y =(e'y + e-iy)
sin y = (ety – e-ly)
Two Distinct Real Roots
1
Real Double Root
2i
1
y = cze21*+ c2xe?2*
5(e +e-Y)
cosh y =
2
1
Complex Conjugate Roots 11 = a + ib 12 = a – ib
sinh y =(ey – e-")
ey = cosh y + i sinh y
e-y = cosh y - i sinh y
y = eax(C1 cos bx + c2 sin bx)
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 3 steps
![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)