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

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SUMMARY

The discussion focuses on solving a second-order nonlinear differential equation defined by the equation D*C''(x) = A*C(x)/[K+C(x)], with initial conditions C(0) = Known and C''(a) = 0. The solution approach involves transforming the equation into the form c''(x) = c' * (dc'/dc) and integrating both sides to derive c'. This method effectively allows for the resolution of the equation by obtaining c' and subsequently integrating to find C(x).

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gsarantop
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Hi, I'm trying to solve this exercise:
0=<x=<a
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)
C''(a)=0
Do you have any idea how I may proceed with this?
 
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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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