# Little confused

1. Oct 11, 2005

### mathmike

hi all i have a bit of a problem here, it has to do with completing the cube.

here is the problem

y''' +y' + 2y = 0

i am trying to sove by the methoed of constant coefficients

2. Oct 11, 2005

### HallsofIvy

Staff Emeritus
So your characteristic equation is r3+ r+ 2= 0.

One of the things I notice immediately is that (-1)3+ (-1)+ 2= 0. Does that help?

3. Oct 11, 2005

### saltydog

So how do you divide r+1 into $r^3+r+2$?

Well r goes into $r^3, r^2$ times right? So that means:

$$r^2(r+1)=r^3+r^2$$

and:

$$(r^3+r+2)-(r^3+r^2)=-r^2+r+2$$

Ok, we got the first one: $r^2$

Now, how do you divide r+1 into $-r^2+r+2$

Keep doin' that to get to the quadratic form of the remaining roots, remainder at end is 0 if -1 is a root. You know how to do this right?

Last edited: Oct 11, 2005