Help from Technology For the DE in Problem, solve analytically to obtain solution curves t...

Help from Technology For the DE in Problem, solve analytically to obtain solution curves through the points (1,1) and (−1, −1). Then, using an appropriate software package, draw the direction field and superimpose your solution curves onto it.

Making Equations Separable Many differential equations that are not separable can be made separable by making a proper substitution. One example is the class of first-order equations with right-hand sides that are functions of the combination y/t (or t/y). Given such a DE

called Euler-homogeneous, let υ = y/t. By the product rule, we deduce from y = υt that

so the equation becomes

which separates into