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Given the following DE: $$2x^2y''+xy'-(x+1)y=0$$
A) Find its indicial equation for Frobenius method.

B)Find two linearly independent Frobenius series solutions using the value of '$m$' obtained from the indicate equation in part A. [ List at least 4 term of each solution].

Please help me with this problem, step by step please. Thank You.

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The first step is to find the indicial polynomial. Substitute, $$y(x)=\sum_{n=0}^{\infty}a_{n}x^{n+r}$$ and try to simplify the equation following the general procedure mentioned here. You should get,

$$r(r-1)+\frac{r}{2}-\frac{1}{2}=0$$

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