9. ty" + y' = 0, 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
100%
Please answer #9
section 3.2
![Exercises 1-15:
In these exercises, the t-interval of interest is -o <t < oo unless indicated otherwise.
(a) Verify that the given functions are solutions of the differential equation.
(b) Calculate the Wronskian. Do the two functions form a fundamental set of solutions?
(c) If the two functions form a fundamental set, determine the unique solution of the
initial value problem.
1. y" – 4y = 0; y1 (1) = e2".
2. y" – y = 0; y1(1) = 2e', y2(t) =e-+3;
3. y" + y = 0; y(t) = 0, y2(t) = sint; y(7/2) = 1, y (7/2) = 1
y2 (t) = 2e-2"; y(0) = 1, y'(0) = -2
y(-1) = 1, y(-1) = 0
4. y" + y = 0; y,(t) = cost, y2(t) = sint; y(7/2) = 1, y'(7/2) = 1
y, (t) = e", y2(t) = te: y(0) = 2, y(0) = 0
6. 2y" – y' = 0; y; (t) = 1, y2(t) = e'2; y(2) = 0, y'(2) = 2
7. y" – 3y + 2y = 0; y1(1) = 2e', y2(t) = e; y(-1) = 1, y'(-1) = 0
5. y" – 4y + 4y = 0;
8. 4y" + y = 0; y1(t) = sin[(t/2) + (7/3)], y2(t) = sin[(t/2) – (/3)];
y(0) = 0, y'(0) = 1
9. ty" + y' = 0, 0<t < o0; y; (f) = In t,
y2(t) = In 3t; y(3) = 0, y'(3) = 3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3afa98d3-5d5f-4802-bbdd-7e6af6547327%2F9e6c5524-b45b-40f9-9d56-7d29560da5e7%2F7ndhq3f_processed.png&w=3840&q=75)
Transcribed Image Text:Exercises 1-15:
In these exercises, the t-interval of interest is -o <t < oo unless indicated otherwise.
(a) Verify that the given functions are solutions of the differential equation.
(b) Calculate the Wronskian. Do the two functions form a fundamental set of solutions?
(c) If the two functions form a fundamental set, determine the unique solution of the
initial value problem.
1. y" – 4y = 0; y1 (1) = e2".
2. y" – y = 0; y1(1) = 2e', y2(t) =e-+3;
3. y" + y = 0; y(t) = 0, y2(t) = sint; y(7/2) = 1, y (7/2) = 1
y2 (t) = 2e-2"; y(0) = 1, y'(0) = -2
y(-1) = 1, y(-1) = 0
4. y" + y = 0; y,(t) = cost, y2(t) = sint; y(7/2) = 1, y'(7/2) = 1
y, (t) = e", y2(t) = te: y(0) = 2, y(0) = 0
6. 2y" – y' = 0; y; (t) = 1, y2(t) = e'2; y(2) = 0, y'(2) = 2
7. y" – 3y + 2y = 0; y1(1) = 2e', y2(t) = e; y(-1) = 1, y'(-1) = 0
5. y" – 4y + 4y = 0;
8. 4y" + y = 0; y1(t) = sin[(t/2) + (7/3)], y2(t) = sin[(t/2) – (/3)];
y(0) = 0, y'(0) = 1
9. ty" + y' = 0, 0<t < o0; y; (f) = In t,
y2(t) = In 3t; y(3) = 0, y'(3) = 3
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
