In my book (Boyce Diprima 2000. 7th ed) page 271 first paragraph it is written that: In all cases it is possible to find at least one solution whether $r_1$ and $r_2$ ( two roots of the indicial equation) differ by integer or the same or complex. If they are differ by an integer the solution corresponds to larger root. Why not smaller root ? I couldnot make sufficient reasoning after playing with indices and sums...
2026-03-27 18:07:49.1774634869
Why does the solution correspond to larger root if we solve 2nd ODE with Frobenius method?
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You can solve for smaller root, but the issue is that sometimes we can find more than one group of the linearly independent solutions at the same time. For example in Find the form of a second linear independent solution when the two roots of indicial equation are different by a integer.