Solving differential equation with accurate solutions?

So I want to solve this differential equations with let's say the initial condition x1 and then I want to solve it for x1+d(d somewhere in 10^-6 range). So how do I solve it? thanks,

Answer 1

[CHANDRA SHEKHAR BESTA]

Use this command, before starting your calculation.

_

format long

Answer 2

[John D'Errico]

This is really a non-question. It is far too generic, so the answer will be of no serious use.

You solve it the same way you solve any ODE. With care in the numerical analysis, which probably means understanding the tools you will use, and understanding ODEs in general. You solve it with the right tool. Of course, often the proper tool depends on the ODE to be solved, etc.

My point is that you are thinking that a distance of 1e-6 is a tiny distance. So scale the problem, transforming things by a factor of 1e-6. Now the distance is 1. Problem solved!

Effectively, instead of using units of kilometers, where a distance might be measured as 1e-6 kilometers, you transform the problem to have units of millimeters. Of course, you still need to do all of the things I discussed before.