Find a power series expansion about x= 0 for a general solution to the given differential equation. Your answer should include a general formula for the coefficients. y' - 2xy = 0 .... 00 y = a, E n= 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Problem Statement:**
Find a power series expansion about \( x = 0 \) for a general solution to the given differential equation. Your answer should include a general formula for the coefficients.

**Differential Equation:**
\[ y' - 2xy = 0 \]

**General Solution Format:**
\[ y = a_0 \sum_{n=0}^{\infty} \boxed{\phantom{x}} \]

*Note: The problem asks you to determine and fill in the coefficient formula in the boxed area.*
Transcribed Image Text:**Problem Statement:** Find a power series expansion about \( x = 0 \) for a general solution to the given differential equation. Your answer should include a general formula for the coefficients. **Differential Equation:** \[ y' - 2xy = 0 \] **General Solution Format:** \[ y = a_0 \sum_{n=0}^{\infty} \boxed{\phantom{x}} \] *Note: The problem asks you to determine and fill in the coefficient formula in the boxed area.*
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