Word Count : 393

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Given the differential equation:  

\[
x^2 y'' + 6x y' + (6 + x^2)y = 0
\]

### Step 1: Assume a Power Series Solution  
Let \( y \) be represented as a power series about \( x = 0 \):  

\[
y = \sum_{n=0}^{\infty} a_n x^n
\]

### Step 2: Compute Derivatives  

First derivative:  

\[
y' = \sum_{n=1}^{\infty} n a_n x^{n-1}
\]

Second derivative:  

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