Graph particular solutions of the following ODE, proceeding as explained. (21) y cos x dx + 1/y dy = 0.
(a) Test for exactness. If necessary, find an integrating factor. Find the general solution u(x, y) = c.
(b) Solve (21) by separating variable. Is this simpler that (a)?
(c) Graph contours u(x, y) = c by your CAS. (Cf. Fig. 16.)
(d) In another graph show the solution curves satisfying y(0) = ±1, ±2, ±3, ±4. Compare the quality of (c) and (d) and comment.
(e) Do the same steps for another non exact ODE of your choice.