# Math Help - Representing DE as systems

1. ## Representing DE as systems

Here is my revision question. I dont know where to start. Can someone please show me how to do this?

2. ## 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 $\left[ \begin{array}{lll}\dot x_1 &=& x_2 \\ \dot x_2 &=& g(x_2, x_1, t) \end{array} \right.$

3. ## Re: Representing DE as systems

So how would i represent this as a 3 dimensional system?

4. ## Re: Representing DE as systems

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?