When you will read this webpage ,then you will find that they have made cases for different types of second order reaction .
In $situation 2A $ of case 2 in the article (eq 1.13 and 1.14) ,they have taken change in concentration of A to be dx/dt instead of
d(a-x)/dt .What is the reason for this ?
Also what I am also finding difficulty is how did they combine the reactants to make it $[A]^2$....... it would mean that individually the concentration of a single reactant A is following 1st order reaction. So the rate constant in disappearence of A should be first order instead of second so what is the reason for this .I t would have make sense for 2A to follow second order instead of just A