# Lipschitz condition, more of like a clarification

1. Sep 27, 2006

### relinquished™

Hello,

I just have one question that's been bothering me. When I reduce a higher ODE to a First ODE, and if I prove that First ODE satisfies the Lipschitz condition, does that mean that the higher ODE has a unique solution (thanks to some other theorem)?

All clarifications are appreciated,

Reli~

2. Sep 27, 2006

### HallsofIvy

Staff Emeritus
Yes. The point is that the higher order de is equivalent to the first order de. You can convert any solution of the first order de to a unique solution of the higher order de. If the solution to the first order de problem is unique then so is the solution to the higher order de.

3. Sep 28, 2006

### relinquished™

Thanks for the clarification Halls. Things are a bit clearer now. :)

Reli~