A Veterinary doctor was examining a sick cat brought by a pet lover. When it was brought to the hospital, it was already dead. The pet lover wanted to find its time of death. He took the temperature of the cat at 11.30 pm which was `94.6^(@)F`. He took the temperature again after one hour, the temperature was lower than the first observation. It was `93.4^(@)F`. The room in which the cat was put is always at `70^(@)F`. The normal temperature of the cat is taken as `98.6^(@)F` when it was alive. The doctor estimated the time of death using Newton law of cooling which is governed by the differential equation: `(dT)/(dt) prop (T − 70),` where `70^(@)F` is the room temperature and T is the temperature of the object at time t. Substituting the two different observations of T and t made, in the solution of the differential equation `(dT)/(dt)`=k(T-70) where k is a constant of proportion, time of death is calculated. Which method of solving a differential equation helped in calculation of the time of death?