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Separation of variables on 2nd order ode

  1. Sep 5, 2012 #1
    Hi all

    Quick one, if one had an equation y' = x on could simply separate the variables and integrate. Now it the equation y'' = x you would use separation of variables what drives this?

    Also

    y'' =0. Is the same as. y''dx =0 dx
    Why is this legal?


    Thanks in advance
     
  2. jcsd
  3. Sep 7, 2012 #2

    HallsofIvy

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    Well, you can always multiply both sides of an equation by the same thing! So, yes, y''= 0 is the same as y''dx= 0dx= 0. And you can now integrate both sides of the equation, with respect to x, to get y'(x)= C where C is a constant of integration. But you did not really need to do that. You know, I hope, that if the derivative of a function is 0, then the function is a constant: if the second derivative of y is 0, the first derivative is a constant.
     
  4. Sep 7, 2012 #3
    Ok re read what I wrote and my main question is not clear

    Why is

    D^2y/Dx^2 = 0 not the same as d^2y =0 dx^2

    On one side u get a line on the other u get something else what is the rigorous explanation
     
    Last edited: Sep 7, 2012
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