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