Does Lipschitz condition on first-order ODE guarantee uniqueness for higher-order ODE?

[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~

 

[HallsofIvy]

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.

 

[relinquished™]

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

Reli~