Let F(x,y,c) := xycy2 + x

"Solve" your ODE (to the extent possible) to characterize the orthogonal trajectories of "F = 0" (that are given by graphs of functions of x). Hint: Your ODE should be separable. You should be able to obtain an equation satised by its solutions that will characterize those solutions, but you probably won't be able to solve it explicitly for y as a function of x.