So the solution to an ODE derived in Heat and Mass Transfer is

$\displaystyle ln(1-x)=c_1z+c_2$ where x=fn(z)

where,

$\displaystyle @z=z_1, x=x_1$ and

$\displaystyle @z=z_2, x=x_2$

Our professor gave us the answer with the applied boundary conditions as follows:

$\displaystyle ((1-x)/(1-x_1))=((1-x_2)/(1-x_1))^n$

where

$\displaystyle n=(z-z_1)/(z_2-z_1)$

which i do not know how to derive at the end!!!

He also gave us a trick which involves manipulating the c1 and c2 constants, as follows:

Let $\displaystyle c_1=ln(k_1)$ & $\displaystyle c_2=ln(k_2)$

Thus

$\displaystyle ln(1-x)=c_1z+c_2$ becomes

$\displaystyle ln(1-x)=ln(k_1)z+ln(k_2)$

Good luck for whoever tries to solve this, I will indeed give you the title of "The Beast" in this forum...I am counting on you guys,

**i need to know the procedure to solve this on my final**