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help with number 8 and please explain the process on how to get the answer

help with number 8 and please explain the process on how to get the answer

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
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help with number 8 and please explain the process on how to get the answer

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
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 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
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