Two simultaneous linear differential equations in variables x(t) and y(t) take the form

These may be solved by differentiating one or other of the equations and substituting an expression for dx/dt or dy/dt into the other equation to form a second order differential equation in x or y. Such systems of differential equations are of importance in the linear theory of equilibria.

Alternatively, the equations can be rewritten as a single matrix equation

This then has the solution

(See exponential of a matrix.)