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Multivariable Calculus

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Sum of the First Five Nonzero Coefficients of Series Solution

MVCALC-XXDAXR

Find the sum of the first five nonzero coefficients of the series solution centered at $x_0 = 0$ of the differential equation:

$$(x^2+1)y'' + xy' + 3y = 0$$
$$y(0) = 18$$
$$y'(0) = 2$$

A

$-\frac32$

B

$\frac32$

C

$\frac{7}{18}$

D

$12$

E

None of the Above