Verify that the indicated expression is an implicit solution of the given differential equation. (dy/dx)2 + 1 = 1/y2 ; (x − 7)2 + y2 = 1
Using implicit differentiation,
(x − 7)2 + y2 = 1
+ 2y dy dx = 0
(dy/dx)2 =
Since (x − 7)2 = 1 − y2, we have that (dy/dx)2 + 1 = 1/y2 .