Originally Posted by

**monster** I'm attepmting to solve a second order partial differential equation using the seperation of variable method, but have gotten up to where i have reduced to ordinary differential equations and has been so long since i did them i'm confused.

If i have say;

X'' - X/(k^2) = 0

And i try a solution of the form X =$\displaystyle e^{(\lambda x)}$

hence X' = $\displaystyle \lambda e^{(\lambda x)} $

and X'' = $\displaystyle \lambda^2 e^{(\lambda x)} $

when substituted in gives;

$\displaystyle \lambda^2 e^{(\lambda x)} - \frac{e^{(\lambda x)}}{k^2} = 0$

hence; $\displaystyle \lambda = + (1/k) or - 1/k $

is this correct up to here? and the following is where i'm confused,

this seems to me to be real distinct solutions hence general solution should be;

X(x) = $\displaystyle A.e^{\frac{x}{k}} +B.e^{\frac{-x}{k}} $

but i remember the lecturer saying that this should be a trig or hyperbolic solution, as there is no complex roots i'm gussing hyperbolics?

Any help would be greatly appreciated, i'm very hazy on this stuff,

Cheers.