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

[gsarantop]

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?

 

[phyzguy]

The trick to solving equations like this, of the form c'' = f(c), is to write $$c''(x) = \frac{dc'}{dx} = \frac{dc'}{dc}\frac{dc}{dx} = c'\frac{dc'}{dc}$$. 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.