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Hi Steve,

Today I was playing with Mathematica, I managed to remove the Sinh^2 and
Cosh^2 but where before I had all cosh and sinh terms with [a t'] I now have
also terms with [2 a t']
Here it is:

 2*t^2 - 2*(x^2 + y^2 + z^2))
+(ax^2 + ay^2 + az^2)*(-3 + 4*Cosh[a*T] - Cosh[2*a*T])
+a^2*(-1 + (ax*x + ay*y + az*z)*(-4 + 4*Cosh[a*T]) + Cosh[2*a*T])
-4*a^3*t*Sinh[a*T] = 0