s instructed, || e-SP(x) dx Y/2 = Y/₁(x) [² (2(x) = -√²/(x) 2: dx (5) to find a second solution y₂(x). Y₁ = x³ x²y" - 5xy' +9y = 0;
s instructed, || e-SP(x) dx Y/2 = Y/₁(x) [² (2(x) = -√²/(x) 2: dx (5) to find a second solution y₂(x). Y₁ = x³ x²y" - 5xy' +9y = 0;
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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Question
![The indicated function \( y_1(x) \) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2,
\[
y_2 = y_1(x) \int \frac{e^{-\int P(x) \, dx}}{y_1^2(x)} \, dx \quad (5)
\]
as instructed, to find a second solution \( y_2(x) \).
\[
x^2 y'' - 5xy' + 9y = 0; \quad y_1 = x^3
\]
\( y_2 = \) [Blank space for solution]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F76aaab3c-5a4a-4ff8-814d-d2e8a1f30217%2Fad8284a0-f782-4522-8011-81936bbb620c%2Fhxh50cq_processed.png&w=3840&q=75)
Transcribed Image Text:The indicated function \( y_1(x) \) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2,
\[
y_2 = y_1(x) \int \frac{e^{-\int P(x) \, dx}}{y_1^2(x)} \, dx \quad (5)
\]
as instructed, to find a second solution \( y_2(x) \).
\[
x^2 y'' - 5xy' + 9y = 0; \quad y_1 = x^3
\]
\( y_2 = \) [Blank space for solution]
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