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Simple question in ODE's

  1. Dec 30, 2009 #1
    1. The problem statement, all variables and given/known data
    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

    2. Relevant equations
    3. The attempt at a solution
  2. jcsd
  3. Dec 30, 2009 #2


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    [tex]y'= dy/dx= 2\sqrt{y}= 2y^{1/2}[/tex]
    [tex]y^{-1/2}dy= 2dx[/tex]
    Integrate to get one solution. Another obvious solution is y(x)= 0.
  4. Dec 30, 2009 #3
    Hey there hallsofIvy...I did it this way too, but I realy thought that we must have a contradiction or something from the existence and uniqueess theorem...NVM...

    TNX a lot for your help!
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