Give the differential equation, as well as the solution, of the irreversible reaction

$2$A $+$ B $->$ Z$,$ whose speed is proportional to the product of concentrations $[$A$]2$

$[$B$]$ and the

reactants are in stoichiometric proportions. The initial concentration of A is $2$a$0$ and

of B a$0.$ Also, give the expression for the half$-$life of the above reaction.

$($Hint: Initial amount of component A equal to $2$a$0$ and component B equal to a$0.$ After

lapse of time t the component A becomes equal to $2$a$0-2$x$.$ To calculate time

half$-$life x $=$ a$0/2.)$