Determining a rate constant of second order?

Question

The reaction 2NO --> N2 + O2 has the following rate law:

-D[NO]/Dt = 2k[NO]^2

After a period of 2.0 x 10^3 s, the concentration of NO falls from an initial value of 2.8 x 10^-3 mol/L to 2.0 x 10^-3 mol/L. What is the rate constant, k?

Answer 1

solve the differential equiation for the rate and it states

[NO]^-1 = 2k +[NO]o^-1 where [NO]o is initial concentration

make sure you understand this and validate my math (I have not solved a differentail equation in well over 25 years and there may be an error). Now solve the above for k

k = {[NO]^-1 -[NO]o^-1}/2 and plug in the numbers from above