An indicial equation, also called a characteristic equation, is a recurrence equation obtained during application of the Frobenius method of solving a second-order ordinary differential equation. The indicial equation is obtained by noting that, by definition, the lowest order term x^k (that corresponding to n = 0) must have a coefficient of zero. 1. If the two roots are equal, only one solution can be obtained. 2. If the two roots differ by a noninteger, two solutions can be obtained. 3. If the two roots differ by an integer, the larger will yield a solution. The smaller may or may not.
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