# Transforming Order of ODE System

Hi
i got a question trying to solve some problems from my schools webpage and encountered a problem where im given 2 RLC-Circuits and the corresponding dgls for the oscilation ( no problem so for all the standart basic E/M stuff)

But then im asked to transform this system of 2 dgl´s of second order to a system of first order ode´s ( think i´ll need 4 of them)

It ´s kind of the same thing like transforming from lagrange to hamilton mechanics ( in a waage sense at least :) )

Could you just test me which technique to use no need for a extensive explanetion of how to do don´t wanna steals one´s time ;) Can look that up in a book.
bye and thanks so far :)

## Answers and Replies

Usually you can transform a second order ode to first order ode by using a Laplace transformation.

I not up on the EE jargon (dgl?) but, if you have a second-order diff. equation, you can turn it into a system of first order diff eq's (say y is a function of x) by replacing u=y and v=y' (so the second-order term y" is replaced by v').
This leads to a matrix form of the problem.
(Try the ode book by Boyce and DiPrima)

thx so far you really helped me out :)