How to Relate b(0) and M in This Secondary Differential Equation?

[Boryna]

Hi, I have a problem with this equation:

d^2b/dz^2= M*(K+c*b)/(k+c*b)

b(1)=1

K,k,c are constans

I need to find a relation between b(0) and M. If it is possible when I resolve this equation and set z = 0?

Thanks in advance.

 

[kosovtsov]

An integrating factor to your ODE is

$$\mu = \frac {db}{dz}$$

So you can find the first integral and then the general solution to your ODE (It'll be in implicit form, unfortunately).