Q$3.$ For the third order irreversible reaction $A+BD$ in a batch reactor, the reaction rate is given $r_D=k{C}_A{C}_B^2.$ Please derive and prove the following relationship is true.

$\frac{1}{C_A^2}-\frac{1}{C_{A0}^2}=2kt,M=1$

$\frac{(C_{A0}-C_{B0})(C_{B0}-C_B)}{C_{B0}{C}_B}+ln\frac{C_{A0}{C}_B}{C_{B0}{C}_A}=(C_{A0}-C_{B0}{)}^{2}kt,M1$