Just a simple question:
Is cosxdy/dx = x non-linear because of cosx?
According to the wiki, a linear differential equation is of the form
where is a linear differential operator.
That is, you apply CB's definition of linearity to the operator, not necessarily to the entire equation. If the equation is homogeneous, they'll turn out to be the same thing. But even a non-homogeneous linear DE does not obey the superposition principle except in its homogeneous solution.
This is my understanding.