Linear System
A system is called "Linear" if for any constants a,b and for any inputs x1(t),x2(t),(x1[n],x2[n]) yielding output y1(t),y2(t) respective's the
Example
For function y=2t+1, its derivitive y'=2 y' is a constant Thus y=2t+1 is a linear system. For function y=sin(t), y'=cos(t) y' is not a constant Thus y=sin(t) is a non-linear system.
