1. The problem statement, all variables and given/known data In the following case: x'(t) = log (3t (x(t) - 2)) does the theorem of existence and unicity guarantee a unique solution for the initial value problem x(3) = 5, justify your answer? 2. Relevant equations x'(t) = log (3t (x(t) - 2)) 3. The attempt at a solution Ok what I would do is take the domain of f(x,t) and the domain of ∂f(x,t)/∂x and then find the common interval and if the initial value problem is within this interval then there is a unique solution. However there is x(t) and t in the function so I don't understand how to find the domain?