Finding Solutions for ODE y'=2*sqrt(|y|) with Initial Condition y(0)=0

[TheForumLord]

Homework Statement

Given this ODE :
y'=2*sqrt(|y|) , y(0)=0 ...
Can we find two different soloutions around (0,0) ? If there are, find them... If there are no two different soloutions around (0,0) - explain why...

Help is needed! TNX

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

$$y'= dy/dx= 2\sqrt{y}= 2y^{1/2}$$
so
$$y^{-1/2}dy= 2dx$$
Integrate to get one solution. Another obvious solution is y(x)= 0.

 

[TheForumLord]

Hey there hallsofIvy...I did it this way too, but I really thought that we must have a contradiction or something from the existence and uniqueess theorem...NVM...

TNX a lot for your help!