Show that the given function is a solution of the differential equation. d²y dy dx dx² dx d²y dx² Substituting checks. d²y dy dx²¹ 8x -7x - 56y= 0, y = c₁e³x + c₂е¯ and y into the original equation gives - 56(c₁e³x + c₂e-7x) = 0. The solution

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)