how to solve secondary differential equations with two unknowns

[sdkdgg]

I got the following equations, φ=f(Z), C is concentration, t is time, Z is distance.
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φ*dC/dt=φ*(d^2 C)/(dZ^2 ) - φ

φ=0.763+0.086e^(-0.216*Z)

How to get and plot C?

 

[pgc01]

Hi
Welcome to the board

I cannot make much sense of your problem. Maybe you can answer some questions and clarify it?

1 -
First question would be: how is this an excel problem?

You were thinking of
- whether there is an add-in to solve differencial equations?
- you were thinking of some numerical method to solve the equations and want to know if that can be made with excel (for ex. using the solver)?
- ...?

2 -
Second question: the first equation, even not knowing what it is about, makes no sense to me. You've got all the term multiplied by φ, which means that you can divide both members of the equation by φ and it will simply disappear.

φ*dC/dt=φ*(d^2 C)/(dZ^2 ) - φ

divide all the equation by φ

dC/dt=(d^2 C)/(dZ^2 ) - 1

this is odd.

3 - third question:

You say secondary differential equations with 2 unknowns but I only see 1 differencial equation, the second one is not even a differential equation, let alone a second order one.
Are you thinking of some mathematical manipulation of the equations that will result in a system of differential equations?

4 - usually this type of problems demand knowing some initial conditions, that allow us to determine the exact solutions. Do you have them?

5 - plot C? what is the domain?



Can you clarify?