E-)E-) (E--) d? + 25 dt2 (6) 3 dt 4 dt y = 0,

How do we know if a differential equation is linear? Describe in the most comprehensive way you know

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 involed) and whether or not the equation is linear. Linearity is important because the structure of 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   for 2 3 and 4 it is also based on the drop down menu (in the picture)