(a) Suppose that A and B are nonzero constants. Show that the equation x2y″ + Ay′ + By = 0 has at most one solution of the form y = xr Σ cnxn. (b) Repeatpart (a) with the equation x3y″ + Axy′ + By = 0. (c) Show that the equation x3y″ + Ax2y′ + By = 0 has no Frobenius series solution. (Suggestion: In each case substitute y = xr Σ cnxn the given equation to determine the possible values of r.)
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