In the first part of the talk, we will discuss linearization of mechanical control systems. In particular, we will study the problem of whether the mechanical and linear structures are compatible. We start with state-space linearization and then discuss feedback linearization. In the second part, we will discuss implicit differential equations and show how they are related with control systems with outputs. Then we will introduce two notions of equivalence of implicit differential equations (internal and external) and study linearization of them in the internal and external sense.