# Representing DE as systems

• January 15th 2012, 07:25 AM
jonnyl
Representing DE as systems
Here is my revision question. I dont know where to start. Can someone please show me how to do this?
• January 15th 2012, 09:35 AM
ILikeSerena
Re: Representing DE as systems
Welcome to MHF, jonnyl! :)

A system of the form $\ddot x = g(\dot x, x, t)$ can be rewritten with $x_1=x$ and $x_2=\dot x$.

From this you get the system $\left[ \begin{array}{lll}\dot x_1 &=& x_2 \\ \dot x_2 &=& g(x_2, x_1, t) \end{array} \right.$
• January 16th 2012, 05:47 AM
jonnyl
Re: Representing DE as systems
So how would i represent this as a 3 dimensional system?
• January 16th 2012, 11:23 AM
ILikeSerena
Re: Representing DE as systems
Quote:

Originally Posted by jonnyl
So how would i represent this as a 3 dimensional system?

To convert the ODE to an autonomous system, you need to eliminate the dependency on the time variable t.
Introduce $x_3=\cos \omega t$.
Now find $\dot x_3$ by using only $x_1,x_2,x_3$. Can you?