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Section4.3Systems Of Equations

Subsection4.3.1First Example

Let us look at the following pair of coupled first order differential equations:

\begin{equation}\frac{dx}{dt} + y(t) = 0\label{men-24}\tag{4.3.1}\end{equation}\begin{equation}\frac{dy}{dt} - x(t) = 0\label{men-25}\tag{4.3.2}\end{equation}

Initial conditions:

\begin{equation}y(0) = 1\label{men-26}\tag{4.3.3}\end{equation}\begin{equation}x(0) = 2\label{men-27}\tag{4.3.4}\end{equation}

You should now be comfortable with defining the variables, the functions, and the initial conditions. The only difference is the use of the desolve_system() method. So let us jump straight in:

Try this for fun:

A controlled explosion!