The indicated function y₁(x) is a solution of the given differential equation. x²y" - 5xy' + 9y = 0; Y1 x³ Use reduction of order or formula (5) in Section 4.2, as instructed. Find the integrating factor. e-SP(x) dx Y2 Y₂₁(x)] Y₂ = y₁(x) = = e -SP(x) dx Find a second solution y₂(x). y ²₁ (x) dx = X (5)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
100%
The indicated function y₁(x) is a solution of the given differential equation.
x²y" - 5xy' + 9y = 0; Y1 = X
x³
Use reduction of order or formula (5) in Section 4.2, as instructed.
Find the integrating factor.
e-SP(x) dx
Y2
Y₁₂(x)]
Y₂ = y₁(x)
=
=
e
-SP(x) dx
Find a second solution y₂(x).
y ²₁ (x)
dx
(5)
Transcribed Image Text:The indicated function y₁(x) is a solution of the given differential equation. x²y" - 5xy' + 9y = 0; Y1 = X x³ Use reduction of order or formula (5) in Section 4.2, as instructed. Find the integrating factor. e-SP(x) dx Y2 Y₁₂(x)] Y₂ = y₁(x) = = e -SP(x) dx Find a second solution y₂(x). y ²₁ (x) dx (5)
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