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DE help please

  1. May 30, 2007 #1
    1. The problem statement, all variables and given/known data

    Given y1=x^2 and y2=1 are two solutions of the DE
    y"=(x/y)y'

    Are the functions -y1 and y1 and y2 also the solutions of the equation?If not why?

    2. Relevant equations
    3. The attempt at a solution

    I cannot see how to proceed.However,I can see that it is a non-linear DE of
    2nd degree where we cannot simply sum the solutions to have another solution...
    That might explain the case that y1+y2 is not a solution...

    what about the first case,i.e -y1?
     
  2. jcsd
  3. May 30, 2007 #2
    Do you end up with an identity when you substitute -y1, (-y1)' and (-y1)'' the DE?
     
  4. May 30, 2007 #3
    OK what I am getting is a wrong thing:-2=2!!!
    So,this shows -y1 cannot be a solution.

    Perhaps I was thinking in unnecessary complicated manner.

    What about the 2nd part? that is y1+y2?
    Am I correct there?
     
  5. May 30, 2007 #4
    Yes you are. You can check by doing what you did for 1.
     
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