I would like to calculate a system of two differential equations in Mathematica using
fx''[x] + a*fx[x] == -I*eta*fy''[x] - b*fy[x], ...
fy[x] are unknown functions. Using
DSolve I can easily find some solutions of the type
fx[x] = C*cosh[x/L] + C*a*sinh[x/L], where
L is a term of the dimension of
The problem is, that the parameters
b in my equations have physical dimension (e.g. meter). From the analysis of the solution the two terms in the result have different physical dimension, which is nonsensical. Another option is that Mathematica rescaled
C so that finally it has dimension of
My question is: Can I somehow control the physical dimensions of the parameters
(a,b) in the differential equations or the constants
C in the result?