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Show the relation is an implicit solution of the DiffEQ

  1. Sep 11, 2014 #1
    1. The problem statement, all variables and given/known data

    Differential equation: 2xyy' = x^2 + y^2
    Relation: y^2 = x^2 - cx
    2. Relevant equations



    3. The attempt at a solution
    Hello, I can normally solve this problems with ease; however, I am having trouble with this particular problem. I have performed the implicit differentiation to get: (2yy' = 2x - c). However, I can't seem to figure out where to go from here. I am thinking that perhaps there is some obvious simplification that I am missing. If somebody can point me in the right direction I'd greatly appreciate it. Thanks.
     
  2. jcsd
  3. Sep 11, 2014 #2

    vela

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    Multiply 2yy' = 2x-c by x so that the lefthand sides look the same and use 2x^2 = x^2+x^2.
     
  4. Sep 11, 2014 #3
    thank you very much, I figured I was missing something somewhat obvious
     
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