# Non-Trivial Solution

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Solve question #3

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

#### Solution Preview

Please see the attachment file.

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.

$2.19