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## Homework Statement

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

http://webwork.math.ncsu.edu/webwork2_files/tmp/equations/21/885ac2eff6f65b363662233870e25e1.png [Broken]

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.)

## The Attempt at a Solution

[itex]\frac{dS}{dt}[/itex] = [itex]\frac{aS}{K + S}[/itex]

[itex]\int[/itex][itex]\frac{K + S}{aS}[/itex] = [itex]\int[/itex]dt

ln(aS)([itex]\frac{S^2}{2}+KS[/itex]) = t

I'm not even sure how to begin to solve for S

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