Example of A Linear System
A two-dimensional system of linear differential equations can be written in the form:
which can be organized into a matrix equation:
where A is the 2 × 2 coefficient matrix above, and x = (x, y) is a coordinate vector of two independent variables.
Such systems may be solved analytically, for this case by integrating:
although the solutions are implicit functions in x and y, and are difficult to interpret.
Read more about this topic: Phase Plane
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—William Cobbett (17621835)