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Differential Equations

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Moderate

Taylor Series of the Solution

DIFFEQ-LD7NXG

Consider the solution for $y''+xy'+3y=0$, satisfying $y(0)=1$, $y'(0)=0$.

In the Taylor series of $y$ about $x=0$, the coefficient of $x^3$, denoted as $a_3$, is: