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

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

Dear Sir, Madam,
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.

I think you forgot to add your attachment.

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.

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

thank you sir for your interesting
so you mean that I have to insert some equation linked between C(x) and F(x) in order to make my equation has only F(x) as a variable .... i got this idea but unfortunately i don;t have an equation linked these variables
which might makes the solution is impossible
is that right or there is another way
someone told me that you can solve it in case of using Range-Kutta method
Regards

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