Suppose r0 is a repeated root of the auxiliary equation ar2 + br + c = 0. Then, as we well know, is a solution to the equation where a, b, and c are constants. Use a derivation similar to the one given in this section for the case when the indicial equation has a repeated root to show that a second linearly independent solution is

# Suppose r0 is a repeated root of the auxiliary equation

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## Solution for problem 18E Chapter 8.5

Fundamentals of Differential Equations | 8th Edition

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Problem 18E

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Suppose r0 is a repeated root of the auxiliary equation