At 12:51 PM 3/29/2017, Schroeppel, Richard wrote:
Easy transform for your 3x equations: Set g(x) = K f(x), with K tbd. Then G(3x) = K f(3x) = 3K f(x) + Kb f(x)^3 = 3 G(x) + (Kb/27) G(x)^3.
Adjust Kb/27 to be whatever you like; I suggest trying +-4.
Indeed! Thanks! (%i1) bar; 3 (%o1) f(3 x) - b f (x) - 3 f(x) (%i2) f(x):=K*sinh(x); (%o2) f(x) := K sinh(x) (%i3) %o1,eval; 3 3 (%o3) - b sinh (x) K + sinh(3 x) K - 3 sinh(x) K (%i4) %/K,expand; 3 2 (%o4) - b sinh (x) K + sinh(3 x) - 3 sinh(x) (%i5) %,K^2=4/b,expand; 3 (%o5) sinh(3 x) - 4 sinh (x) - 3 sinh(x) (%i6) %,trigreduce,expand; (%o6) 0 So our b is simply a weird way to scale sinh().