Differential Equations - Fick's Law

[kiwiatheart]

Homework Statement

A cell contains a solute at a concentration of Ct and the concentration of the same substance outside the cell is a constant, k. By Fick's law, if ct and k are unequal, solute moves across the cell wall at a rate proportional to the difference between ct and k, towards the region of lower concentration.

a) Write down the differential equation that is satisfied by ct.
b) solve the differential equation for ct, with the initial condition C0 > A
c) Sketch the solution for A > k and k> A

Homework Equations

The Attempt at a Solution

I got as far as dS/dt = M (Ct - k) (M is a constant) I then got Be^(mt) = Ct - K. I don't think I understand differential equations because this is supposed to be very simple.

Thank you everyone!
P.S This is maths for biology students.

 

[vela]

Homework Statement

A cell contains a solute at a concentration of Ct and the concentration of the same substance outside the cell is a constant, k. By Fick's law, if ct and k are unequal, solute moves across the cell wall at a rate proportional to the difference between ct and k, towards the region of lower concentration.

a) Write down the differential equation that is satisfied by ct.
b) solve the differential equation for ct, with the initial condition C0 > A
c) Sketch the solution for A > k and k> A

What is A supposed to be? It seems to appear out of nowhere.

The Attempt at a Solution

I got as far as dS/dt = M (Ct - k) (M is a constant) I then got Be^(mt) = Ct - K. I don't think I understand differential equations because this is supposed to be very simple.

What is S? How is it related to ct?

It's not a good idea to keep changing cases of the variable, e.g. m vs. M, as upper and lower case letters are often used to denote different quantities. Pick one case and stick with it for each variable.