I've only just completed high school, but I have a decent grasp on basic undergrad maths/physics. After hours and hours of paper and mental calculations, I still can't see a way of solving Newton's law of gravitation for the path of a body given inital position/velocity i.e. the second order non-linear differential equation r'' = -GM/(r^2). Can somebody please put my mind at ease by telling me that it cannot be done or showing me how. T'would be much appreciated as I am getting sick of pages that go from Newton's law to conic sections in one jump.