Solving a Cube Problem with Constant Coefficients

[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

 

[HallsofIvy]

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?

 

[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?