- #1

- 188

- 0

^{III}+y

^{II}-y

^{I}-y = 0

I used the characteristic equation and got:

r

^{3}+r

^{2}-r = 0

r (r

^{2}+r-1) = 0

Which means that r = 0 is one root,

And the other factors from the polynomial are (-1-Sqrt(5))/2 and (-1+Sqrt(5))/2

This means that the final answer would be:

y = C

_{1}Exp(0x) + C

_{2}Exp((-1-Sqrt(5))/2) + C

_{3}Exp((-1+Sqrt(5))/2)

Then I'd simplify from there, but I checked my answer in the back of the book, and it says that I'm wrong. It says the answer is

y = C

_{1}Exp(x) + C

_{2}Exp(-x) + C

_{3}x Exp(-x)

I also solved the equation using Mathematica and also got the answer that the book states.

Where did I go wrong?