How do you determine the properties of a differential equation? If I was given a differential equation of the form $$y'(t) + a(t)y(t) = x(t)$$ how would I be able to decide its linearity, time-invariance, and causality?
If a system is represented by a differential equation then it must be LINEAR.
If the coefficients of differential equation are function of time then it is time variant otherwise time invariance.
For causality and stability we will need its transfer function for any comment.