This system of differential equations is a set of coupled, first-order, nonlinear differential equations. Here, x(t), y(t) and z(t) are functions of time (t), and m, n, l are constants.
The equations in the system are:
1) dx/dt = my - nz
2) dy/dt = nz - lx
3) dz/dt = lx - my
Unfortunately, the method for solving these equations analytically isn't straightforward due to their complexity. This type of system can often arise in the context of physics problems, such as the motion of objects under some forces, which is a common setting where they pop up.
In such cases, it's often necessary to resort to numerical methods for finding approximate solutions. This can be achieved by using a method like Euler's method, or more sophisticated methods like the Runge-Kutta methods.
Remember that these methods won't give a closed-form solution. Instead, they will provide a numerical approximation to the solution, giving the values of x, y, and z at discrete points in time. The accuracy of these solutions depends on the step size and the specific method used, with smaller step sizes generally leading to more accurate solutions.
To summarize, while we can't solve this system analytically due to its complexity, we can use numerical methods to find an approximate solution.