The indicated function y, (x) is a solution of the given differential equation. Use reduction of order or formúla (5) in Section 4.2, eP(x) dx Y2 = Y;(x)- xp. (5) as instructed, to find a second solution y,(x). x²y" – 9xy' + 25y = 0; y, = x Y2
The indicated function y, (x) is a solution of the given differential equation. Use reduction of order or formúla (5) in Section 4.2, eP(x) dx Y2 = Y;(x)- xp. (5) as instructed, to find a second solution y,(x). x²y" – 9xy' + 25y = 0; y, = x 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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![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 \( y_2(x) \).
\[
x^2y'' - 9xy' + 25y = 0; \quad y_1 = x^5
\]
\[
y_2 = \underline{\hspace{2cm}}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9bf7f6f8-9470-47f0-a3a4-f3c052528216%2Fca79b895-2668-4a23-8872-89e413352854%2Ftmbg0rj_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,
\[
y_2 = y_1(x) \int \frac{e^{-\int P(x) \, dx}}{y_1^2(x)} \, dx \quad (5)
\]
as instructed, to find a second solution \( y_2(x) \).
\[
x^2y'' - 9xy' + 25y = 0; \quad y_1 = x^5
\]
\[
y_2 = \underline{\hspace{2cm}}
\]
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