Consider the second order equation below. Find a recursion equation for the coefficients of the pow series solution. Express the coefficient an+1 in terms of n and an. −2xy"+(2x − 3)y'+5y = 0 [Note: complete the recursion equation by only entering the function in n that is multiplied by an produce an+1 for all n ≥ 0.] an+1 = ·an; n ≥0
Consider the second order equation below. Find a recursion equation for the coefficients of the pow series solution. Express the coefficient an+1 in terms of n and an. −2xy"+(2x − 3)y'+5y = 0 [Note: complete the recursion equation by only entering the function in n that is multiplied by an produce an+1 for all n ≥ 0.] an+1 = ·an; n ≥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
![**Problem Statement:**
Consider the second order equation below. Find a recursion equation for the coefficients of the power series solution. Express the coefficient \( a_{n+1} \) in terms of \( n \) and \( a_n \).
\[
-2xy'' + (2x - 3)y' + 5y = 0
\]
**Note:** Complete the recursion equation by only entering the function in \( n \) that is multiplied by \( a_n \) to produce \( a_{n+1} \) for all \( n \geq 0 \.
\[
a_{n+1} = \boxed{\phantom{answer}} \cdot a_n; \quad n \geq 0
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb48e445-6f22-4655-aae5-a52568300bfa%2F435c22c7-d308-4512-b3b3-712c532ee626%2Fbrg64ei_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Consider the second order equation below. Find a recursion equation for the coefficients of the power series solution. Express the coefficient \( a_{n+1} \) in terms of \( n \) and \( a_n \).
\[
-2xy'' + (2x - 3)y' + 5y = 0
\]
**Note:** Complete the recursion equation by only entering the function in \( n \) that is multiplied by \( a_n \) to produce \( a_{n+1} \) for all \( n \geq 0 \.
\[
a_{n+1} = \boxed{\phantom{answer}} \cdot a_n; \quad n \geq 0
\]
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The question says n>0 but your solution says n>1.
Is this the correct answer for the problem ? It asks for n>0.
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