Each of the differential equations x3 y y 0 and x 2 y (3x 1)y y 0 has an irregular

Chapter 5, Problem 36

(choose chapter or problem)

Each of the differential equations

\(x^{3} y^{\prime \prime}+y=0 \quad \text { and } \quad x^{2} y^{\prime \prime}+(3 x-1) y^{\prime}+y=0\)

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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