It can be to classify a differential equation, so that we can predict the techniques that might 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: 1. (1+y2)(d2y/dt2)+t(dy/dt)+y=et2. t^2(d2y/dt2)+t(dy/dt)+2y=sin t3. (d3y/dt3)+t(dy/dt)+(cos2(t))y=t^34. y''-y+y2=0