1. Show that y6 + x - 2 = 0 is an implicit solution to dy/dx = - 1/6y on the interval (- infinity, 2 ). 2. Show that xy9 - xy9 cos x = 1 is an implicit solution to the differential equation
dy/dx = (- x sin x + cos x - 1 )y / 9 (x - x cos x ) on the interval (0, 2 pi ).
3. To verify the solution and the interval, convert y8 + x - 3 = 0 to explicit function(s).
y = 8 x + 3