Difficult# Find the Sum of the First Nonzero Coefficients of Series Solution

MVCALC-N1XAUC

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

$$(x^2-1) \frac{d^2y}{dx^2} + x \frac{dy}{dx} + x^2 y = 0$$

$$y(0) = 6$$

$$y'(0) = 3$$