Difficult# 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:

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

$$y(0) = 18$$

$$y'(0) = 2$$