(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

use characteristic equation to solve y^{(4)}-y=0

2. Relevant equations

characteristic equation would be r^{4}-1=0

3. The attempt at a solution

my question is related to the number of roots. with r^4 that generally means there will be 4 roots?

but theres only 3? 1,0,-1.... my calculator doesnt solve polynomials higher then third order so im just looking for clarification on this.

would there be 4 roots and just one of them is repeated? so then the solution would be something like y(x)=c_{1}e^{r1x}+c_{2}e^{r2x}+(c_{3}+c_{4}x)e^{r3x}...

or are there just 3 roots and its y(x)=c1e^r1x + c2e^r2x + c3e^r3x ??

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# Simple characterisitic equation clarification

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