I'm trying to find the gen. solution to the equation y''''-8y'=0(adsbygoogle = window.adsbygoogle || []).push({});

I found the characteristic polynomial by plugging in e^{rt}as a solution to y.

I got,

r^4-8r=0

I simplified to get

r*(r^3-8)

Thus one root is 0, for the other 3 i must find the cubed root of 8.

I know the answer is 2*e^{2m*pi*i/3}for m=0,1,2

How do I arrive at that answer?

I tried the following:

Represent 8 as 8=8[cos(2*pi)+i*sin(2*pi)]=8*e^{i*pi}

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# 4th order differential equation

**Physics Forums | Science Articles, Homework Help, Discussion**