It can be helpful to classify a differential equation, so that we can predict the techniques that might help us to find a function which solves the equation. Two classifications are the order of the equation -- (what is the highest number of derivatives involved) and whether or not the equation is linear Linearity is important because the structure of the the family of solutions to a linear equation is fairly simple. Linear equations can usually be solved completely and explicitly. Determine whether or not each equation is linear: d d' - 1. dt4 d'y dy = 1 dt ? dt3 dt? 2. (1+ y?) dy d'y +t: ? + y = et dt2 dt dy v 3. + ty? = 0 ? dt - 4. y" y + y? = 0 ?