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March 30, 2017

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Given the differential equations:
(sin x)y′′+ xy′+(x − 1/9)
y = 0:
• Determine all the regular singular points for the Eq.;
• Derive the indicial equation corresponding to each regular point;
• Determine the form of two linearly independent solutions near each
of regular singular points.
• Give the behavior of solutions as x → 0.

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