I'm currently a third year undergrad electrical engineering student studying linear control system and very much confused regarding the term "linearity".
- Does the term "A linear ODE" necessarily mean that the system it is describing has to be a "linear system"?
- Given a differential equation, can one directly test the linearity (Homogeneity and Superposition) of the equation without first finding its solution?
If you can explain the concepts in a more simpler manner instead of rigorous math, that would be appreciated. But if it's necessary to understand the math behind it, I'll try my best. Thanks!