I have found a toy implementation of RK-Dopri(4,5), written in Python.
I am concerned however, about line 118:
y = y + h * (b1*K1+b3*K3+b4*K4+b5*K5+b6*K6)
Has the term
b2*K2 been omitted on purpose? I have a feeling that it is not, given (1.8) in Hairer, Wanner and Norsett:
Can you confirm?