as instructed, to find a second solution y₂(x). x²y" + 2xy' - 6y = 0; y₁ = x² Y₂ =
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 \( y_2(x) \).
\[
x^2 y'' + 2x y' - 6y = 0; \quad y_1 = x^2
\]
\[
y_2 = \, \boxed{}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F76aaab3c-5a4a-4ff8-814d-d2e8a1f30217%2F49c85a33-f4ff-4570-a87f-1b9f18badc16%2F3y63yj_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 \( y_2(x) \).
\[
x^2 y'' + 2x y' - 6y = 0; \quad y_1 = x^2
\]
\[
y_2 = \, \boxed{}
\]
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