# [SOLVED]converting ODE to a system of ODEs

#### dwsmith

##### Well-known member
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
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
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
Thanks typo. I trying to find the attraction basin for this system in another post. Are you familiar with that stuff?