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 =
hence X' =
and X'' =
when substituted in gives;
hence;
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) =
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.