Thread: second order differential equation with two variables, please have a look

1. second order differential equation with two variables, please have a look

I hope you are doing well..
At first let me introduce myself.. I am Mudhar an international Ph.D student in the University of Bradford, United Kingdom working in modeling of reverse osmosis units for wastewater treatment. Actually I have stacked with a solution of second order differential equation. Unfortunately I couldn't find a way to solve this problem ... please. AS expected, In case if I can solve this equation this might guide me to construct my new model.
My equation has two variables in the right side of equation as mentioned below please
d2F(x) / dx2 ) = alpha * F(x)) / [ (Beta - (gama * C(x)) ]
where alpha , beta , gama are constants but F(x) and C(x) are variable with x dimension I have boundary conditions for this equation as

at x =0, F(x) = F(inlet), C(x) = C(inlet) at x = L , F(x) = F(outlet) , C(x) = C(outlet)
Please do me a fevour and have a look at my attachment and you definitely will let me know if there is a possible solution or not.
I will be waiting for your response even if takes a long time
Accept my apologize for inconvenience
Warm regards
Mudhar

2. Re: second order differential equation with two variables, please have a look

Hey mudharalaubedy.

3. Re: second order differential equation with two variables, please have a look

Oh sorry this is because i write down my specific problem even that i will do it now and thanks for reminding me and hope you might solve my threat
regards
mudhar

4. Re: second order differential equation with two variables, please have a look

So your equation is $\displaystyle \frac{d^2F}{dx^2}=\frac{\alpha F(x)}{\beta- \gamma C(x)}$?

And you have the values of both F and C at x= 0 and x= L?

The problem is that you have two different unknown functions, F and C, with only one equation. Generally, you cannot solve a single equation for two unknowns. For example, you could choose a number of different functions for C, as long as they satisfy the boundary conditions, and solve for F.