(a) Show that y Superscript 8 Baseline plus x minus 3 equals 0 is an implicit solution to StartFraction dy Over dx EndFraction
equals negative StartFraction 1 Over 8 y Superscript 7 EndFraction on the interval (negative infinity comma 3 ). (b) Show that xy Superscript 9 Baseline minus xy Superscript 9 Baseline cosine x equals 1 is an implicit solution to the differential equation StartFraction dy Over dx EndFraction equals StartFraction (negative x sine x plus cosine x minus 1 )y Over 9 (x minus x cosine x )EndFraction on the interval (0 comma 2 pi ). (c) To verify the solution and the interval, convert y Superscript 8 Baseline plus x minus 3 equals 0 to explicit function(s). yequals RootIndex 8 StartRoot x plus 3 EndRoot (Use a comma to separate answers as needed.)
