It was stated (on page 7) that "Norder sets of initial values are especially appropriate for N-order differential equations." The following problems illustrate one reason this is true. In particular, they demonstrate that, if y satisfies some N-order initial-value problem, then it automatically satisfies particular higher-order sets of initial values. Because of this, specifying the initial values for ym) with m 2 N is unnecessary and may even lead to problems with no solutions. a. Assume y satisfies the first-order initial-value problem i. Using the differential equation along with the given value for y(1), determine what value y'(1) must be ii. Is it possible to have a solution to i. Find the value of y(0) and of y(0) ii. Is it possible to have a solution to 3ry+2 with y(1)=2. that also satisfies both y(1)=2 and y'(1)-4? (Give a reason.) iii. Differentiate the given differential equation to obtain a second-order differential equation. Using the equation obtained along with the now known values for y(1) and y'(1), find the value of y(1). iv. Can we continue and find y(1), y) (1)....? b. Assume y satisfies the second-order initial-value problem that also satisfies all of the following: =3zy+z¹ +4-8y=0 with y(0) 3 and y(0) = 5. +44-8y=0 y (0) 3, y(0)-5 and "(0)=0 ?
It was stated (on page 7) that "Norder sets of initial values are especially appropriate for N-order differential equations." The following problems illustrate one reason this is true. In particular, they demonstrate that, if y satisfies some N-order initial-value problem, then it automatically satisfies particular higher-order sets of initial values. Because of this, specifying the initial values for ym) with m 2 N is unnecessary and may even lead to problems with no solutions. a. Assume y satisfies the first-order initial-value problem i. Using the differential equation along with the given value for y(1), determine what value y'(1) must be ii. Is it possible to have a solution to i. Find the value of y(0) and of y(0) ii. Is it possible to have a solution to 3ry+2 with y(1)=2. that also satisfies both y(1)=2 and y'(1)-4? (Give a reason.) iii. Differentiate the given differential equation to obtain a second-order differential equation. Using the equation obtained along with the now known values for y(1) and y'(1), find the value of y(1). iv. Can we continue and find y(1), y) (1)....? b. Assume y satisfies the second-order initial-value problem that also satisfies all of the following: =3zy+z¹ +4-8y=0 with y(0) 3 and y(0) = 5. +44-8y=0 y (0) 3, y(0)-5 and "(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
partb
Expert Solution
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 4 steps with 26 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,