# Reconstructing my notes

1. May 28, 2005

I'm trying to rewrite my notes from my differential equations class last week. my proffesor asked us to write the charastic equation of this:$$y''-4y' +5y =0$$ is this correct?
$$e^{2t}(C_1\cos{t} + C_2\sin{t})$$

2. May 28, 2005

### HallsofIvy

Staff Emeritus
No, it's not- it's not even an equation! I would suggest you look up "characteristic equation" in your text book.

3. May 28, 2005

i meant this.$$y=e^{2t}(C_1\cos{t} + C_2\sin{t})$$

4. May 28, 2005

### arildno

The characteristic equation is what you elsewhere call the auxiliary equation, if I'm not mistaken.

5. May 28, 2005

### mathwonk

x^2 - 4x + 5, i.e. make every derivative a power, so you get x^2 -4x + 5x^0

or just substitute y = e^(rt) then perform the derivatives in the given differential equation and you get the characteristic equation out front in terms of the variable r this time.