Multivariable Calculus

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Moderate

Find the Recursive Relation for the Coefficients of Power Series

MVCALC-PXRGKV

Find the recursive relation for the coefficients of the power series solution centered at $x_0 = 0$ for the differential equation:

$$y'' + xy' + y= 0$$

A

$2a_2 + a_0 = 0$ and $(n+2)(n+1)a_{n+2} + (n+1)a_n = 0$ for $n=1,2,3,\ldots$.

B

$a_2 + a_0 = 0$ and $(n+2)(n+1)a_{n+2} + (n+1)a_n = 0$ for $n=1,2,3,\ldots$.

C

$(n+2)(n+1)a_{n+2} + (n+1)a_n = 0$ for $n=0,1,2,\ldots$.

D

$2a_2 + a_0 = 0$ and $(n+2)(n+1)a_{n+2} + na_n = 0$ for $n=1,2,3,\ldots$.

E

None of the Above