Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
For Problems 1-10, a differential equation and one solution are given. Use d'Alembert's reduction of order method to find a second linearly independent solution. What is the general solution of the differential equation? Differential equation 1. y" - y =0 2. y" + y = 0 3.- 4y + 4y= 0 4. y" + y = 0 5. " + y = 0 6. xy" 2(x + 1)y' + 4y= 0 7. ²y" - 6y = 0 8. xy" - xy' + y = 0 Solution Y₁(x) = e y₁(x) = sin x 3₁(x) = ²x y₁(x) = 1 Y₁(x) = 1 y₁(x) = Y/₁(x) = y₁(x) = x =x²

For Problems 1-10, a differential equation and one solution are given. Use d'Alembert's reduction of order method to find a second linearly independent solution. What is the general solution of the differential equation? Differential equation 1. y" - y =0 2. y" + y = 0 3.- 4y + 4y= 0 4. y" + y = 0 5. " + y = 0 6. xy" 2(x + 1)y' + 4y= 0 7. ²y" - 6y = 0 8. xy" - xy' + y = 0 Solution Y₁(x) = e y₁(x) = sin x 3₁(x) = ²x y₁(x) = 1 Y₁(x) = 1 y₁(x) = Y/₁(x) = y₁(x) = x =x²

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

help find number 7 and please explain with step

For Problems 1–10, a differential equation and one solution are given. Use d’Alembert’s reduction of order method to find a second linearly independent solution. What is the general solution of the differential equation? **Differential equation and Solution:** 1. \( y'' - y = 0 \) - \( y_1(x) = e^x \) 2. \( y'' + y = 0 \) - \( y_1(x) = \sin x \) 3. \( y'' - 4y' + 4y = 0 \) - \( y_1(x) = e^{2x} \) 4. \( y'' + y' = 0 \) - \( y_1(x) = 1 \) 5. \( y'' + y' = 0 \) - \( y_1(x) = 1 \) 6. \( xy'' - 2(x+1)y' + 4y = 0 \) - \( y_1(x) = e^x \) 7. \( x^2y'' - 6y = 0 \) - \( y_1(x) = x^3 \) 8. \( x^2y'' - xy' + y = 0 \) - \( y_1(x) = x \) For each problem, the task is to find a second linearly independent solution using the given technique, and then determine the general solution of the differential equation.
Transcribed Image Text:For Problems 1–10, a differential equation and one solution are given. Use d’Alembert’s reduction of order method to find a second linearly independent solution. What is the general solution of the differential equation? **Differential equation and Solution:** 1. \( y'' - y = 0 \) - \( y_1(x) = e^x \) 2. \( y'' + y = 0 \) - \( y_1(x) = \sin x \) 3. \( y'' - 4y' + 4y = 0 \) - \( y_1(x) = e^{2x} \) 4. \( y'' + y' = 0 \) - \( y_1(x) = 1 \) 5. \( y'' + y' = 0 \) - \( y_1(x) = 1 \) 6. \( xy'' - 2(x+1)y' + 4y = 0 \) - \( y_1(x) = e^x \) 7. \( x^2y'' - 6y = 0 \) - \( y_1(x) = x^3 \) 8. \( x^2y'' - xy' + y = 0 \) - \( y_1(x) = x \) For each problem, the task is to find a second linearly independent solution using the given technique, and then determine the general solution of the differential equation.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

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