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Ordinary Differential Equations

  1. Jan 9, 2013 #1
    1. The problem statement, all variables and given/known data

    y = 2xy' + y(y')2; y2 = C1 (x + C1 /4)



    2. The attempt at a solution

    I thought that I could take the first equation and set it equal to zero. But the C1 in the second equation is throwing me off.

    Am I supposed to set the second equal to C1?
     
    Last edited: Jan 9, 2013
  2. jcsd
  3. Jan 9, 2013 #2

    HallsofIvy

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    Are you saying that you want to show that [itex]y= \pm\sqrt{C_1(x+ \frac{C_1}{4})}[/itex] satisfies [/itex]y= 2xy'+ y(y')^2[/itex]?

    Just find the derivative of y and plug it into the equation.
     
  4. Jan 9, 2013 #3
    Sorry the second equation is y2, but I think I see what you are saying.
     
  5. Jan 9, 2013 #4

    HallsofIvy

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    Yes, that's why I took the square root to get y.
     
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