Question

Find the general solution of the homogeneous equation.

y'''''-3y''''+3y'''-3y''+2y'=0

Answer 1

Assume a solution of the form y=e^(at)

Answer 2

well if I did that then that would mean that every root was different, how do you know every root is different?

Answer 3

Why not just check? See what the roots of the characteristic polynomial yield.

Answer 4

well i would definitely like to, and could probably take it from there, but i am not sure how to break apart something with that high of an order

Answer 5

What do you mean? Try solving the 5th degree polynomial. See if it factors or something

Answer 6

yup, i dont know how to factor that

Answer 7

ohh, nevermind, i think i can get it, take 1 -1 2 -2 and check those, and r=0 already.

Answer 8

Either use some software or use good old rational root theorem, test, and divide.

Answer 9

thanks for the help.

Answer 10

Glad to help