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Non-linear ODE: y'=(y-1)^2 + 0.01

  1. Aug 31, 2010 #1
    1. The problem statement, all variables and given/known data

    y' = ( y - 1 )^2 +0.01 y(0)=1

    (trying out latex)
    [tex]y' = (y-2)^{2} + 0.01; y(0)=1[/tex]

    2. Relevant equations

    Separation of variables, Right?

    3. The attempt at a solution

    The solution is is y(x)=1+0.1 Tan (0.1x)

    How did they get this? I did separation of variables and got:

    dx = ( 1/(y-1)^2 + 100 )dy

    integrating gets:

    x = -1/(y-1) +100y + C

    Tangent...is not here. What am I doing wrong here?
  2. jcsd
  3. Sep 1, 2010 #2


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    Staff Emeritus
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    Check your algebra. You're making a very elementary mistake.
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