# 2nd order homogeneous linear diff eq

1. Mar 13, 2012

### arl146

1. The problem statement, all variables and given/known data
y'' + y' - 2y = 0

2. Relevant equations

3. The attempt at a solution
I think this is extremely simple. hopefully i am correct. i said the 'auxiliary' equation is r2 + r - 2 = (r+2)(r-1) = 0
the roots are r = 1, -2
so the solution is y=c1ex + c2e-2x

correct?

2. Mar 13, 2012

### S_Happens

Yes, it's correct.

3. Mar 13, 2012

### LCKurtz

Yes. You could easily check that yourself by plugging it back into the DE and see if it works.

4. Mar 13, 2012

### arl146

just substitute the solution in for y in the diff eq? how does that work to show me if i am right?

nevermind!

5. Mar 13, 2012

### Staff: Mentor

Take the first and second derivatives of your solution, and substitute them and the solution into the differential equation. The result should be identically equal to zero.

6. Mar 13, 2012

### Ray Vickson

Here is a *very important* hint: Always check this for yourself, by substituting in your y and seeing whether it obeys the DE; that is, compute y', y'', etc. That should be your very first step, and it is something that has been drummed into the head of every physics/math student during the last 100 years.

RGV