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Question: Find the recurrence relation at x=0 for the following ODE $$2xy^{′′} +(3−x)y′ −y = 0 $$

My Attempt:

I know $x=0$ is a regular singular point therefore I must use the Frobenius method. However whilst attempting the frobenius method, my indicial equation gives me $r=-1$, which is only one solution. Am I making an error in calculating the indicial equation or is it correct?

Thank you

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Try again. The indicial equation is $r^2 + r/2 = 0$. This has two roots, neither being $-1$.

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