Power Series Solution

Calculus Level 2

Find the second value in terms of a 0 a_{0} for the following differential equation (Eq. A) using the following assumption,

y ( x ) = k = 0 a k x k . y(x)= \sum_{k=0}^\infty\ a_{k}x^{k}.

d 2 y d x 2 + x d y d x + y ( x ) = 0 ( E q . A ) \frac{d^2 y}{dx^2}+x\frac{dy}{dx}+y(x)=0 (Eq. A)

a 0 8 \frac{-a_{0}}{8} a 1 3 \frac{-a_{1}}{3} a 0 945 \frac{-a_{0}}{945}

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