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

$$(x^2-1) \frac{d^2y}{dx^2} + x \frac{dy}{dx} + x^2 y = 0$$$$y(0) = 6$$$$y'(0) = 3$$

$\frac{23}{6}$

$-\frac{23}{6}$

$10$

$\frac{19}{2}$

No solution exists.