# Exponential Solution of Cubic Equation

1. Jul 9, 2011

, Dear Fellows
I need to find the solution of cubic equation in exponential form which is written in a research article

If EQUATION is

(k^6-A k^4+B k^2+E)Y(z)=0

and solution given is as,

Y(z)=M exp(-k_1z)

where M is a constant and k_1 is solution of the above equation.

2. Jul 9, 2011

### HallsofIvy

I can't make heads or tails out of what you have written. The equation you write:
(k^6-A k^4+B k^2+E)Y(z)=0 simply tells us that, for some z, Y(z)= 0. It does NOT say that this is a cubic equation and Y could be anything.

3. Jul 9, 2011

### jambaugh

It looks like you were solving a 6th order differential equation in Y?
$$[D_z^6 - A D_z^4 + D_z k^2 + E]Y(z)=0$$
There is a cubic formula but it's pretty messy, especially if you are leaving A,B, and E arbitrary. Google "cubic formula" and you'll find many links. The wikipedia article is a good reference: http://en.wikipedia.org/wiki/Cubic_function" [Broken]

Last edited by a moderator: May 5, 2017