Mathematical Methods in the Physical Sciences · Problem 33

ORDINARY DIFFERENTIAL EQUATIONS — Mary Boas

Mathematics — Methods · orthogonal-trajectories

Problem

Find the orthogonal trajectories of the family of curves

y = kx^n

. (Assume that

n

is a given number; the different curves of the family have different values of

k

.) Sketch several of the given curves and several of their orthogonal trajectories.