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the four ode should be:

sage: de1=diff(E,t)==-k1ES+k2ES+kiES sage: de2=diff(ES,t)==k1ES-kiES-k2ES sage: de3=diff(S,t)==-k1ES+kiES sage: de4=diff(P,t)==k2ES

the four ode should be:

sage: de1=diff(E,t)==-k1ES+k2ES+kiES de1=diff(E,t)==-k1*E*S+k2*ES+ki*ES sage: de2=diff(ES,t)==k1ES-kiES-k2ES de2=diff(ES,t)==k1*E*S-ki*ES-k2*ES sage: de3=diff(S,t)==-k1ES+kiES de3=diff(S,t)==-k1*E*S+ki*ES sage: de4=diff(P,t)==k2ES de4=diff(P,t)==k2*ES