The Linearity Principle is a fundamental property of systems of the form dY/dt = AY. Howev...

The Linearity Principle is a fundamental property of systems of the form dY/dt = AY. However, you should not assume that it is true for systems that are not of this form, no matter how simple. For example, consider the system

The following computations show that the Linearity Principle does not hold for this system.

(a) Show that is a solution to this system.

(b) Show that 2Y(t) is not a solution. An Extended Linearity Principle that applies to systems.