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7. (15 points) Consider the differential equation 2 xy + (2 + x2 )y' + 2xy = 0. A) Find all the regular singular points.

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7. (15 points) Consider the differential equation 2 xy" + (2 + x2 )y' + 2xy = 0. A) Find all the regular singular points. Justify your answer. Regular singular points: B) Find the indicial equation and one Frobenius Series Solution. Also find a form for the second linearly independent solution (for the second solution you do not have to evaluate the coefficients). Indicial equation: y1 = y2 =

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