This is a really helpful video. I tried rewriting keplers equations in 3 dimensions, which i thought would be an easy extension from what you did - 3 2nd order ODE's means 6 1st order ODE's with 6 initial conditions - but it was not easy. Why don't you consider the gravitational parameter, mu, in your example for keplers equation? I find when i add mu to your code, then the graph falls apart.
Hello. Thanks for the nice video. I would like to know how can we solve a boundary value problem. I mean if the initial condition is at the non-zero value of an independent variable.
Hi. Thanks for your comment. Here's the link to another tutorial. I hope it helps you. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-0-6LID5gZhQ.html
Not every differential equation has an analytical answer. But you can always try. Learn how to use dsolve command for the exact solution of ODEs. Here's the link: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-liN7C9Fs9ew.html