The indicated function y,(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2. e SP(x) dx Y2 =Y,(x) xp. (5) as instructed, to find a second solution y,(x). x²y"- xy' + 17y = 0; y, = x sin(4 In(x)) Y2
The indicated function y,(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2. e SP(x) dx Y2 =Y,(x) xp. (5) as instructed, to find a second solution y,(x). x²y"- xy' + 17y = 0; y, = x sin(4 In(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,
\[
y_2 = y_1(x) \int \frac{e^{-\int P(x) \, dx}}{y_1^2(x)} \, dx \tag{5}
\]
as instructed, to find a second solution \( y_2(x) \):
\[
x^2y'' - xy' + 17y = 0; \quad y_1 = x \sin(4 \ln(x))
\]
\[ y_2 = \boxed{\phantom{y}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9bf7f6f8-9470-47f0-a3a4-f3c052528216%2F1f25043d-9029-4c20-8746-32452ad5067d%2Fwnar043_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,
\[
y_2 = y_1(x) \int \frac{e^{-\int P(x) \, dx}}{y_1^2(x)} \, dx \tag{5}
\]
as instructed, to find a second solution \( y_2(x) \):
\[
x^2y'' - xy' + 17y = 0; \quad y_1 = x \sin(4 \ln(x))
\]
\[ y_2 = \boxed{\phantom{y}} \]
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