It isn't difficult to find the electric field of a dipole. However, it is tricky to find the field lines. All points of a field line have to be parallel to the electric field at those points. A tangent, which is the derivative, is parallel. We can hence formulate the equation for a field line as the solution to a first order differential equation. I have already done so, but I haven't been able to solve it. Google has not been my friend either. Does anyone know of the equations that describe the field lines?