$$\begin{aligned}& \bigl(e_{p}^{R} \bigr)'(t) = - \bigl(c_{p}(t)+d_{p}(t)\bigr)e_{p}^{R}(t) +\sum_{q=1}^{n} \bigl({a}_{pq}^{R}(t) \bigl(f_{q}^{R}\{t,y\} -f_{q} ^{R}\{t,x\} \bigr) \\& \hphantom{\bigl(e_{p}^{R} \bigr)'(t) =}{}-{a}_{pq}^{I}(t) \bigl(f_{q}^{I} \{t,y\}-f_{q}^{I}\{t,x\} \bigr) -{a} _{pq}^{J}(t) \bigl(f_{q}^{J}\{t,y\}-f_{q}^{J} \{t,x\} \bigr) \\& \hphantom{\bigl(e_{p}^{R} \bigr)'(t) =}{}-{a}_{pq}^{K}(t) \bigl(f_{q}^{K} \{t,y\}-f_{q}^{K}\{t,x\} \bigr) \bigr) + \sum _{q=1}^{n} \bigl({b}_{pq}^{R}(t) \bigl(g_{q}^{R}\{t,y\} \\& \hphantom{\bigl(e_{p}^{R} \bigr)'(t) =}{}-g_{q}^{R}\{t,x\} \bigr)-{b}_{pq}^{I}(t) \bigl(g_{q}^{I}\{t,y\}-g_{q} ^{I}\{t,x\} \bigr)-{b}_{pq}^{J}(t) \bigl(g_{q}^{J}\{t,y\} \\& \hphantom{\bigl(e_{p}^{R} \bigr)'(t) =}{}-g_{q}^{J}\{t,x\} \bigr)-{b}_{pq}^{K}(t) \bigl(g_{q}^{K}\{t,y\}-g_{q} ^{K}\{t,x\} \bigr) \bigr) \\& \hphantom{\bigl(e_{p}^{R} \bigr)'(t) =}{}+\sum_{q=1}^{n} \bigl({p}_{pq}^{R}(t)h_{q}^{R} \{t,e\}-{p}_{pq} ^{I}(t)h_{q}^{I} \{t,e\}-{p}_{pq}^{J}(t)h_{q}^{J} \{t,e\} \\& \hphantom{\bigl(e_{p}^{R} \bigr)'(t) =}{}-{p}_{pq}^{K}(t)h_{q}^{K} \{t,e\} \bigr)+\sum_{q=1}^{n} \bigl( {q}_{pq}^{R}(t)\bar{h}_{q}^{R} \{t,\sigma ,e\}-{q}_{pq}^{I}(t)\bar{h} _{q}^{I}\{t,\sigma ,e\} \\& \hphantom{\bigl(e_{p}^{R} \bigr)'(t) =}{}-{q}_{pq}^{J}(t)\bar{h}_{q}^{J} \{t,\sigma ,e\} -{q}_{pq}^{K}(t) \bar{h}_{q}^{K} \{t,\sigma ,e\} \bigr), \\& \bigl(e_{p}^{I} \bigr)'(t) = - \bigl(c_{p}(t)+d_{p}(t)\bigr)e_{p}^{I}(t) +\sum_{q=1}^{n} \bigl({a}_{pq}^{R}(t) \bigl(f_{q}^{I}\{t,y\}-f_{q}^{I} \{t,x\} \bigr) \\& \hphantom{\bigl(e_{p}^{I} \bigr)'(t) =}{}+{a}_{pq}^{I}(t) \bigl(f_{q}^{R} \{t,y\}-f_{q}^{R}\{t,x\} \bigr)+{a}_{pq} ^{J}(t) \bigl(f_{q}^{K}\{t,y \}-f_{q}^{K}\{t,x\} \bigr) \\& \hphantom{\bigl(e_{p}^{I} \bigr)'(t) =}{}-{a}_{pq}^{K}(t) \bigl(f_{q}^{J} \{t,y\}-f_{q}^{J}\{t,x\} \bigr) \bigr) + \sum _{q=1}^{n} \bigl({b}_{pq}^{R}(t) \bigl(g_{q}^{I}\{t,y\} \\& \hphantom{\bigl(e_{p}^{I} \bigr)'(t) =}{}-g_{q}^{I}\{t,x\} \bigr) +{b}_{pq}^{I}(t) \bigl(g_{q}^{R}\{t,y\}-g_{q} ^{R}\{t,x\} \bigr)+{b}_{pq}^{J}(t) \bigl(g_{q}^{K}\{t,y\} \\& \hphantom{\bigl(e_{p}^{I} \bigr)'(t) =}{}-g_{q}^{K}\{t,x\} \bigr)-{b}_{pq}^{K}(t) \bigl(g_{q}^{J}\{t,y\}-g_{q} ^{J}\{t,x\} \bigr) \bigr) \\& \hphantom{\bigl(e_{p}^{I} \bigr)'(t) =}{}+\sum_{q=1}^{n} \bigl({p}_{pq}^{R}(t)h_{q}^{I} \{t,e\}+{p}_{pq} ^{I}(t)h_{q}^{R} \{t,e\} +{p}_{pq}^{J}(t)h_{q}^{K} \{t,e\} \\& \hphantom{\bigl(e_{p}^{I} \bigr)'(t) =}{}-{p}_{pq}^{K}(t)h_{q}^{J} \{t,e\} \bigr) +\sum_{q=1}^{n} \bigl( {q}_{pq}^{R}(t)\bar{h}_{q}^{I} \{t,\sigma ,e\}+{q}_{pq}^{I}(t)\bar{h} _{q}^{R}\{t,\sigma ,e\} \\& \hphantom{\bigl(e_{p}^{I} \bigr)'(t) =}{}+{q}_{pq}^{J}(t)\bar{h}_{q}^{K} \{t,\sigma ,e\}-{q}_{pq}^{K}(t) \bar{h}_{q}^{J} \{t,\sigma ,e\} \bigr), \\& \bigl(e_{p}^{J} \bigr)'(t) = - \bigl(c_{p}(t)+d_{p}(t)\bigr)e_{p}^{J}(t) +\sum_{q=1}^{n} \bigl({a}_{pq}^{R}(t) \bigl(f_{q}^{J}\{t,y\}-f_{q}^{J} \{t,x\} \bigr) \\& \hphantom{\bigl(e_{p}^{J} \bigr)'(t) =}{}+{a}_{pq}^{J}(t) \bigl(f_{q}^{R} \{t,y\}-f_{q}^{R}\{t,x\} \bigr)-{a}_{pq} ^{I}(t) \bigl(f_{q}^{K}\{t,y \}-f_{q}^{K}\{t,x\} \bigr) \\& \hphantom{\bigl(e_{p}^{J} \bigr)'(t) =}{}+{a}_{pq}^{K}(t) \bigl(f_{q}^{I} \{t,y\}-f_{q}^{I}\{t,x\} \bigr) \bigr) + \sum _{q=1}^{n} \bigl({b}_{pq}^{R}(t) \bigl(g_{q}^{J}\{t,y\} \\& \hphantom{\bigl(e_{p}^{J} \bigr)'(t) =}{}-g_{q}^{J}\{t,x\} \bigr) +{b}_{pq}^{J}(t) \bigl(g_{q}^{R}\{t,y\}-g_{q} ^{R}\{t,x\} \bigr)-{b}_{pq}^{I}(t) \bigl(g_{q}^{K}\{t,y\} \\& \hphantom{\bigl(e_{p}^{J} \bigr)'(t) =}{}-g_{q}^{K}\{t,x\} \bigr) +{b}_{pq}^{K}(t) \bigl(g_{q}^{I}\{t,y\}-g_{q} ^{I}\{t,x\} \bigr) \bigr) \\& \hphantom{\bigl(e_{p}^{J} \bigr)'(t) =}{}+\sum_{q=1}^{n} \bigl({p}_{pq}^{R}(t)h_{q}^{J} \{t,e\}+{p}_{pq} ^{J}(t)h_{q}^{R} \{t,e\} -{p}_{pq}^{I}(t)h_{q}^{K} \{t,e\} \\& \hphantom{\bigl(e_{p}^{J} \bigr)'(t) =}{}+{p}_{pq}^{K}(t)h_{q}^{I} \{t,e\} \bigr) +\sum_{q=1}^{n} \bigl( {q}_{pq}^{R}(t)\bar{h}_{q}^{J} \{t,\sigma ,e\}+{q}_{pq}^{J}(t)\bar{h} _{q}^{R}\{t,\sigma ,e\} \\& \hphantom{\bigl(e_{p}^{J} \bigr)'(t) =}{}-{q}_{pq}^{I}(t)\bar{h}_{q}^{K} \{t,\sigma ,e\} +{q}_{pq}^{K}(t) \bar{h}_{q}^{I} \{t,\sigma ,e\} \bigr), \\& \bigl(e_{p}^{K} \bigr)'(t) = - \bigl(c_{p}(t)+d_{p}(t)\bigr)e_{p}^{K}(t) +\sum_{q=1}^{n} \bigl({a}_{pq}^{R}(t) \bigl(f_{q}^{K}\{t,y\}-f_{q}^{K} \{t,x\} \bigr) \\& \hphantom{\bigl(e_{p}^{K} \bigr)'(t) = }{}+{a}_{pq}^{K}(t) \bigl(f_{q}^{R} \{t,y\}-f_{q}^{R}\{t,x\} \bigr)+{a}_{pq} ^{I}(t) \bigl(f_{q}^{J}\{t,y \}-f_{q}^{J}\{t,x\} \bigr) \\& \hphantom{\bigl(e_{p}^{K} \bigr)'(t) = }{}-{a}_{pq}^{J}(t) \bigl(f_{q}^{I} \{t,y\}-f_{q}^{I}\{t,x\} \bigr) \bigr) + \sum _{q=1}^{n} \bigl({b}_{pq}^{R}(t) \bigl(g_{q}^{K}\{t,y\} \\& \hphantom{\bigl(e_{p}^{K} \bigr)'(t) = }{}-g_{q}^{K}\{t,x\} \bigr) +{b}_{pq}^{K}(t) \bigl(g_{q}^{R}\{t,y\}-g_{q} ^{R}\{t,x\} \bigr)+{b}_{pq}^{I}(t) \bigl(g_{q}^{J}\{t,y\} \\& \hphantom{\bigl(e_{p}^{K} \bigr)'(t) = }{}-g_{q}^{J}\{t,x\} \bigr) -{b}_{pq}^{J}(t) \bigl(g_{q}^{I}\{t,y\}-g_{q} ^{I}\{t,x\} \bigr) \bigr) \\& \hphantom{\bigl(e_{p}^{K} \bigr)'(t) = }{}+\sum_{q=1}^{n} \bigl({p}_{pq}^{R}(t)h_{q}^{K} \{t,e\}+{p}_{pq} ^{K}(t)h_{q}^{R} \{t,e\}+{p}_{pq}^{I}(t)h_{q}^{J} \{t,e\} \\& \hphantom{\bigl(e_{p}^{K} \bigr)'(t) = }{}-{p}_{pq}^{J}(t)h_{q}^{I} \{t,e\} \bigr) +\sum_{q=1}^{n} \bigl( {q}_{pq}^{R}(t)\bar{h}_{q}^{K} \{t,\sigma ,e\} +{q}_{pq}^{K}(t)\bar{h} _{q}^{R}\{t,\sigma ,e\} \\& \hphantom{\bigl(e_{p}^{K} \bigr)'(t) = }{}+{q}_{pq}^{I}(t)\bar{h}_{q}^{J} \{t,\sigma ,e\}-{q}_{pq}^{J}(t) \bar{h}_{q}^{I} \{t,\sigma ,e\} \bigr), \end{aligned}$$
.