In a chemical reaction in which a compound X is formed from a compound Y and other substances, the masses of X and Y present at time

*t* are

*x* and

*y* respectively. The sum of the two masses is constant and at any time the rate at which

*x* s increasing is proportional to the product of the two masses at that time. Show that the equation governing the reaction is of the form

and interpret the constant

*a*. If

at time t=0, find in terms of

*k* and

*a* the time at which

I have completed the first part where

*a* is the sum of

*x* and

*y*.

For the next part I know that I have to solve the differential equation and plug the values of

*t* and

*x*.

Then I used partial fractions to integrate

Now I don't know how to proceed, and I can't get the equation right to find the A.

Thanks