Analytical solution to the simultaneous Michaelis-Menten and second-order kinetics problem

An analytic solution is presented for the simultaneous substrate elimination problem that combines Michaelis-Menten (MM) consumption with an irreversible homo-dimerization process. The implicit solution involves logarithm and inverse tangent functions and perfectly agrees with the numerical solution of the differential equation. A solution is also presented for the generalized dynamical problem that simultaneously combines MM kinetics with first and second-order processes. The exact expressions for the half-life and the area under the curve are also presented for these problems.