Final answer:
The statement is false because both linear and non-linear systems may have varied numbers of equilibrium points; the actual number depends on the systems' differential equations.
Step-by-step explanation:
The statement 'a linear system with constant coefficients has one equilibrium solution, a non-linear system has two or three equilibriums' is false. Linear systems can have a unique equilibrium point, no equilibrium at all, or infinitely many equilibria, depending on whether the system is consistent and independent, inconsistent, or consistent and dependent.
Similarly, non-linear systems may have any number of equilibria, which can be none, one, or many, and these equilibria may be stable, unstable, or neutral. Equilibrium points of systems are determined by the solutions to the system's differential equations, and the nature of these solutions can vary widely in both linear and non-linear systems.