Consider the differential equationx3y+ xy+ y = 0,where and
Chapter 5, Problem 20(choose chapter or problem)
Consider the differential equationx3y+ xy+ y = 0,where and are real constants and = 0.(a) Show that x = 0 is an irregular singular point.(b) By attempting to determine a solution of the form n=0anxr+n, show that the indicialequation for r is linear and that, consequently, there is only one formal solution of theassumed form.(c) Show that if / = 1, 0, 1, 2, ... , then the formal series solution terminates and thereforeis an actual solution. For other values of /, show that the formal series solution hasa zero radius of convergence and so does not represent an actual solution in any interval.
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