Dormand-Prince RK5(4)7

\begin{align} \begin{array}{c|ccccccc} & & & & & & & \\ \frac{1}{5} & \frac{1}{5} & & & & & & \\ \frac{3}{10} & \frac{3}{40} & \frac{9}{40} & & & & & \\ \frac{4}{5} & \frac{44}{45} & - \frac{56}{15} & \frac{32}{9} & & & & \\ \frac{8}{9} & \frac{19372}{6561} & - \frac{25360}{2187} & \frac{64448}{6561} & - \frac{212}{729} & & & \\ 1 & \frac{9017}{3168} & - \frac{355}{33} & \frac{46732}{5247} & \frac{49}{176} & - \frac{5103}{18656} & & \\ 1 & \frac{35}{384} & & \frac{500}{1113} & \frac{125}{192} & - \frac{2187}{6784} & \frac{11}{84} & \\ \hline & \frac{35}{384} & & \frac{500}{1113} & \frac{125}{192} & - \frac{2187}{6784} & \frac{11}{84} & \\ & \frac{5179}{57600} & & \frac{7571}{16695} & \frac{393}{640} & - \frac{92097}{339200} & \frac{187}{2100} & \frac{1}{40} \end{array}\end{align}