Linear Systems and Linear Differential Equations

[tiredryan]

Are all linear differential equations considered linear systems? Does the "linear" in both terms reference to the same characteristics?

http://en.wikipedia.org/wiki/Linear_system
http://en.wikipedia.org/wiki/Linear_differential_equation

 

[Maru]

Yes. The question of linearity requires that a system must be closed under addition, scalar multiplication, and contain zero to be considered linear. A linear differential equation and a linear system are linear under these same qualities. In fact, linear differential equations can create a linear system which models a "subspace" that satisfies these properties as well.