1. The problem statement, all variables and given/known data For y'=1/(x+y), sketch a direction field and the solution through y(0)=0. 2. Relevant equations I'm confused as to why there is a solution through y(0) - I thought that the existence theorem says that if y' is continuous in a box, then there are solutions through all points in the box. 3. The attempt at a solution y' is not continuous in the box surrounding the y=-x line. So why does a solution exist there? Is y' actually continuous there? It approaches negative infinity from one side and positive infinity from the other.