and then I get that d squared Y DT squared is negative Y so I recognize from that that we're looking at a sinusoidal basis of solutions and from that you can guess and check the corresponding coefficients and we get that we have this circular orbit where the only real thing that changes exactly what this the circle looks like is the initial conditions so if you initialize right on the origin you'll stay on the origin but if you initialize off the origin you never get any closer to it so a gradient descent goes into an orbit