Each of the differential equations x 3 y'' + y = 0 and x 2 y'' +

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Each of the differential equations

x3y'' + y = 0 and x2y'' + (3x  1)y' + y = 0


has an irregular singular point at x = 0. Determine whether the method of Frobenius yields a series solution of each differential equation about x = 0. Discuss and explain your findings.

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