2nd order homogeneous linear diff eq

[arl146]

Homework Statement

y'' + y' - 2y = 0

Homework Equations

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=c₁e^x + c₂e^-2x

correct?

 

[S_Happens]

Yes, it's correct.

 

[LCKurtz]

Homework Statement

y'' + y' - 2y = 0

Homework Equations

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=c₁e^x + c₂e^-2x

correct?

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

 

[arl146]

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

nevermind!

 

[Mark44]

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.

 

[Ray Vickson]

Homework Statement

y'' + y' - 2y = 0

Homework Equations

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=c₁e^x + c₂e^-2x

correct?

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