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

find three independent solutions using complex exponentials, but express answer in real form.

d^3(f(t))/dt^3 - f(t) = 0

2. Relevant equations

3. The attempt at a solution

after taking the derivative of z = Ce^(rt) three times

I put it in the following form:

Ce^(rt)(r^3 -1) = 0

and solved for r:

r^3 = 1

1 = e^(i*0)

and so

r = e^(i*0) = 1

1 is one of the solutions right? but I don't understand how it's possible to find 3 independent solutions to that differential equation.

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# Homework Help: Third Order DE Using Complex Exponential

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