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Find the first three nonzero terms of the series solution centered at $x_0 = 0$ for the differential equation:

$$(x-1)y'' - xy = 0$$
$$y(0) = 1$$
$$y'(0) = 1$$

A

$y(x) = 1 + x + \frac16x^2 + \cdots$.

B

$y(x) = 1 + x + \frac23x^3 + \cdots$.

C

$y(x) = 1 + x + \frac16x^3 + \cdots$.

D

$y(x) = 1 + x - \frac23x^3 + \cdots$.

E

None of the Above

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