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The indicated function y₁(x) is a solution of the given differential equation. x²y" - xy' + 5y = 0; Y₁ = x cos(2 In(x)) Use reduction of order or formula (5) in Section 4.2, as instructed. Y₂ = y₁(x) Find the integrating factor. e-SP(x) dx Y₂ /. = e-SP(x) dx e x²(x) Find a second solution y₂(x). dx (5)

The indicated function y₁(x) is a solution of the given differential equation. x²y" - xy' + 5y = 0; Y₁ = x cos(2 In(x)) Use reduction of order or formula (5) in Section 4.2, as instructed. Y₂ = y₁(x) Find the integrating factor. e-SP(x) dx Y₂ /. = e-SP(x) dx e x²(x) Find a second solution y₂(x). dx (5)

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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The indicated function y₁(x) is a solution of the given differential equation. x²y" - xy' + 5y = 0; Y₁ = x cos(2 In(x)) Use reduction of order or formula (5) in Section 4.2, as instructed. √₂(X) / Y₂ = y₁(x) 2 Y2 Find the integrating factor. e-SP(x) dx е = e-SP(x) dx y ²₁ (x) Find a second solution y₂(x). dx (5)
Transcribed Image Text:The indicated function y₁(x) is a solution of the given differential equation. x²y" - xy' + 5y = 0; Y₁ = x cos(2 In(x)) Use reduction of order or formula (5) in Section 4.2, as instructed. √₂(X) / Y₂ = y₁(x) 2 Y2 Find the integrating factor. e-SP(x) dx е = e-SP(x) dx y ²₁ (x) Find a second solution y₂(x). dx (5)
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