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Separable Differential Equation

  1. Jan 29, 2012 #1
    y' = (x)/(1+2y)

    y(-1) = 0

    trying to find the answer I do the following:

    multiply both sides by (1+2y)
    (1+2y) * dy/dx = x

    i subtract 1 from both sides.. but for some reason this is wrong? why?

    2y * dy/dx = x - 1

    2y dy = x-1 dx

    integrate..

    y^2 = (x^2-x+C)/2

    y = sqrt((x^2-x+C)/2) )

    this however is wrong I was not suppose to subtract the 1 from both sides.. what exactly is wrong with doing that?
     
    Last edited: Jan 29, 2012
  2. jcsd
  3. Jan 29, 2012 #2

    ehild

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    Re: Seperable Differnetail Equation

    If you subtract 1 from both sides it will be (1+2y) * dy/dx-1 = x-1.

    (1+2y) * dy/dx = x is not the same as 2y * dy/dx = x - 1 as both 1 and 2y is multiplied by dy/dx in the original equation.

    ehild
     
  4. Jan 29, 2012 #3
    Re: Seperable Differnetail Equation

    even if its multiplied by it like that is?

    I mean I am seeing it in my mind sort of like

    1+5a = b
    in which I would think to solve such an algebraic equation it would be more like

    -1 on both sides
    5a=b-1 ?
     
  5. Jan 29, 2012 #4

    ehild

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    Re: Seperable Differnetail Equation

    Do you know what are parentheses for? I just wonder how you subtract 2 from (2+5)10.

    ehild
     
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