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Finding solution to second order non linear dif. equation with IV

  1. Jun 17, 2010 #1
    Hi, I'm trying to solve this exercise:
    D*C''(x)= A*C(x)/ [K+C(x)]
    D, A and K are constants
    and we know the following IV:
    C(0)= Known (number)
    Do you have any idea how I may proceed with this?
  2. jcsd
  3. Jun 17, 2010 #2


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    Science Advisor

    The trick to solving equations like this, of the form c'' = f(c), is to write [tex] c''(x) = \frac{dc'}{dx} = \frac{dc'}{dc}\frac{dc}{dx} = c'\frac{dc'}{dc}[/tex]. Then, since c' dc'/dc = f(c), c' dc' = f(c) dc, you can integrate both sides and solve for c', which you can then integrate a second time to get the final result.
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