Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Consider the ordinary differential equation y" (x) = 4y(x) + 4, y(0) = y'(0) = 1, (d) which is second order (because of the second derivative), not first order. So we may not directly employ our methods. However, let z(x) be the function given by z(x) = y'(x) + 2y(x). 6.a Assuming y(x) is a solution to (d), determine a differential equation for z(x) (involving z(x) and z'(x) but not y(x) or its derivatives) as well as its initial value z(0). Hint: First compute z'(x) in terms of the derivatives y" (x) and y'(x). Then use (d) to re-express y"(x). 6.b Solve for z(x) in the previous problem. 6.c Use your solution for z(x) to solve for y(x) by solving (z) for y with initial condition y(0) = 1.

Consider the ordinary differential equation y" (x) = 4y(x) + 4, y(0) = y'(0) = 1, (d) which is second order (because of the second derivative), not first order. So we may not directly employ our methods. However, let z(x) be the function given by z(x) = y'(x) + 2y(x). 6.a Assuming y(x) is a solution to (d), determine a differential equation for z(x) (involving z(x) and z'(x) but not y(x) or its derivatives) as well as its initial value z(0). Hint: First compute z'(x) in terms of the derivatives y" (x) and y'(x). Then use (d) to re-express y"(x). 6.b Solve for z(x) in the previous problem. 6.c Use your solution for z(x) to solve for y(x) by solving (z) for y with initial condition y(0) = 1.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
Consider the ordinary differential equation y"(x) = 4y(x) + 4, y(0) = y'(0) = 1, (d) which is second order (because of the second derivative), not first order. So we may not directly employ our methods. However, let z(x) be the function given by z(x) = y'(x) + 2y(x). (z) 6.a Assuming y(x) is a solution to (d), determine a differential equation for z(x) (involving z(x) and z'(x) but not y(x) or its derivatives) as well as its initial value z(0). Hint: First compute z'(x) in terms of the derivatives y"(x) and y'(x). Then use (d) to re-express y"(x). 6.b Solve for z(x) in the previous problem. 6.c Use your solution for z(x) to solve for y(x) by solving (z) for y with initial condition y(0) = 1.
Transcribed Image Text:Consider the ordinary differential equation y"(x) = 4y(x) + 4, y(0) = y'(0) = 1, (d) which is second order (because of the second derivative), not first order. So we may not directly employ our methods. However, let z(x) be the function given by z(x) = y'(x) + 2y(x). (z) 6.a Assuming y(x) is a solution to (d), determine a differential equation for z(x) (involving z(x) and z'(x) but not y(x) or its derivatives) as well as its initial value z(0). Hint: First compute z'(x) in terms of the derivatives y"(x) and y'(x). Then use (d) to re-express y"(x). 6.b Solve for z(x) in the previous problem. 6.c Use your solution for z(x) to solve for y(x) by solving (z) for y with initial condition y(0) = 1.
Expert Solution
steps

Step by step

Solved in 6 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS