Let $S(t)$ represent the amount of a chemical reactant present at time $t$, where $t \geq 0$. Assume that $S(t)$ can be determined by solving the initial value problem

$$S^{\,\prime} = -\frac{a S}{K + S} \ \mathrm{and} \ S(0) = S_0,$$
where $a, K$, and $S_0$ are positive constants. Obtain an implicit solution of the initial value problem. (The differential equation, often referred to as the Michaelis-Menten equation, arises in the study of biochemical reactions.)

Enter the constant $S_0$ as S0 (with a zero, not the letter O).

help (equations)