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Non-Trivial Solution

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https://brainmass.com/math/numerical-analysis/non-trivial-solution-366125

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Problem:
Show that the equation can posses a non trivial solution which vanishes at and only if  is such that , and that corresponding to such a characteristic number , any multiple of the function is a solution with the required properties.

Solution:

We need to perform a function change in order to bring the equation to one of the known standard forms:
( 1)
 ( 2)
We try now a variable change of form
( 3)
 ( 4)
 ...

Solution Summary

A non trivial solution is discussed.

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