The indicated function y. (x) is a solution of the given differential eguation. Use reduction of order or formula (5) in Section 4.2, e-SP(x) dx xp- (5) as instructed, to find a second solution y,(x). xy" + y' = 0; Y, = In x
The indicated function y. (x) is a solution of the given differential eguation. Use reduction of order or formula (5) in Section 4.2, e-SP(x) dx xp- (5) as instructed, to find a second solution y,(x). xy" + y' = 0; Y, = In x
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 \( y_1(x) \) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, as instructed, to find a second solution \( y_2(x) \).
\[
y_2 = y_1(x) \int \frac{e^{-\int P(x) \, dx}}{y_1^2(x)} \, dx \tag{5}
\]
Given:
\[ xy'' + y' = 0; \quad y_1 = \ln x \]
Find \( y_2 = \) [box for answer].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9bf7f6f8-9470-47f0-a3a4-f3c052528216%2F6b314799-0337-4a9f-b76e-be2cc251143a%2Facb3tom_processed.jpeg&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, as instructed, to find a second solution \( y_2(x) \).
\[
y_2 = y_1(x) \int \frac{e^{-\int P(x) \, dx}}{y_1^2(x)} \, dx \tag{5}
\]
Given:
\[ xy'' + y' = 0; \quad y_1 = \ln x \]
Find \( y_2 = \) [box for answer].
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