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[SOLVED] converting ODE to a system of ODEs

dwsmith

Well-known member
Feb 1, 2012
1,673
Given $x''-x+x^3+\gamma x' = 0$.

Is the below correct? Can I do this? The answer is yes.

Let $x_1 = x$ and $x_2 = x'$. Then $x_1' = x_2$.
\begin{alignat}{3}
x_1' & = & x_2\\
x_2' & = & x_1 - x_1^3 + \gamma x_2
\end{alignat}

Then I have the above linear system from the given ODE.
 
Last edited:

Ackbach

Indicium Physicus
Staff member
Jan 26, 2012
4,193
Given $x''-x+x^3+\gamma x' = 0$.

Is the below correct? Can I do this? The answer is yes.

Let $x_1 = x$ and $x_2 = x'$. Then $x_1' = x_2$.
\begin{alignat}{3}
x_1' & = & x_2\\
x_2' & = & x_1 - x_1^3 + \gamma x_2
\end{alignat}

Then I have the above linear system from the given ODE.
Second equation should be
$$x_{2}'=x_{1}-x_{1}^{3}-\gamma x_{2}.$$
 

dwsmith

Well-known member
Feb 1, 2012
1,673
Second equation should be
$$x_{2}'=x_{1}-x_{1}^{3}-\gamma x_{2}.$$
Thanks typo. I trying to find the attraction basin for this system in another post. Are you familiar with that stuff?
 

Sudharaka

Well-known member
MHB Math Helper
Feb 5, 2012
1,621
Thanks typo. I trying to find the attraction basin for this system in another post. Are you familiar with that stuff?
I think your question is answered >>here<<.