Wow, I have no idea wtf i did. But I found an answer in about 5 lines for part ii. of T = -8/3
Here is what I did, and to be honest, I was just fooling around:
You have k/T, k/(T+2), k/(T+3.5)
This is simply substituting into dx/dt = k/t from part i. This can be done because x = 0, x = 1, x =...