The functions y(x) = 1/16 x 4 , - < x < and have the same domain but are clearly different. See the following figure

The functions y(x) = 1/16 x⁴, -ˆž < x < ˆž and

 

have the same domain but are clearly different. See the following figure (a) and (b), respectively. Show that both functions are solutions of the initial-value problem dy/dx = xy^1/2, y(2) = 1 on the interval (ˆž,ˆž). Resolve the apparent contradiction between this fact and the last sentence in Example 5.

(0, ) y. y. (2, 1) (2, 1) (a) (b)