Double Roots
The previous example involved an indicial polynomial with a repeated root, which only gave one solution to the given differential equation. In general, the Frobenius method gives two independent solutions provided that the indicial equation's roots are unique.
If the root is repeated, or the roots differ by an integer, then the second solution can be found by the equation:
Where is the first solution and the coefficients are to be determined.
Read more about this topic: Frobenius Method
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