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## Homework Statement

Solve the following differential equations/initial value problem:

y^(4) - y'' - 2y' +2y = 0 Hint: e^-x sinx is a solution

## Homework Equations

I was attempting to solve this problem by using a characteristic equation.

## The Attempt at a Solution

y'''' -y'' -2y' + 2y = 0 --> r^4 -r^2 -2r +2 = 0

r^2(r^2 - 1) -2(r - 1) = 0

r^2 (r+1)(r-1) -2(r-1) = 0

(r^2(r+1) -2)(r-1) = 0

from this I get r = 1, but I know there are more solutions; How do I solve for the other solutions? And then write it as the solution?