Hello everyone,

Could someone please help me with this problem. It is related to chemical reactions but the behaviour can be described by differential equations. I've simplified the model to the equations you see below.

Lets say there are have two reactions which can be described by the equations:

1: dy/dt = -a*y

2: dy/dt = -b*y

whereaandbare constants.

Integration gives:

1: y(t) = y(0) * exp(-a*t)

2: y(t) = y(0) * exp(-b*t)

Now we perform an experiment where both systems are present so the observed behaviour can be described by:

3: dy/dt = -a*y -b*y

and integrated:

3: y(t) = y(0) * exp(-(a + b)*t)

Now what I want to know is the following:

After the experiment I obtain results described by3. I know the background reaction is described by2. However I am only interested in the exact results of reaction1. How can I extract the exact information of1out of3as if2was never present. In othe words I need to correct3to obtain the actual behaviour I'm interested in.

I thought it would be simple substraction/addition for instance in the simplest approach one could say to just 'correct' reaction3like:

4: dy/dt = -a*y - b*y + b*y

however this equation (when plotted) does not produce the same outcome as1because it does not account for the change in y caused by reaction2.

So it looks like that: dy/dt = -a*y - b*y + b*y is not the same as dy/dt = -a*y

And that is where my mathematical knowledge ends