# MATLAB: Basic ODE question

differential equationsode

So…it's been quite a while since I solved any systems of ODEs and I am admittedly very rusty. I am hoping there is a simple answer to this question:
I have a coupled system of ODEs:
dA/dc=-0.5*(2-v)*(1-v^2)/(1-v)
and
dv/dc=-1.5*(5-v)*(1-v^2)/(3-v)
Solve from c=[0 1]
Initial conditions: Ao=100, vo=0.5
How can I set this up in a Matlab function? Thanks for any advice!

#### Best Answer

1. Write a function that defines the rate equations. The system should now look like z' = f(c,z), where z = [A;v]. Write your function file so that it takes c and a vector z as inputs, and returns a vector dz that represents the derivatives ([A';v'])
2. Use ode45 to solve the system, giving a function handle to you function from step 2 as input, as well as the vector of start and end values for c and the initial conditions z0 = [A0;v0].
3. Extract the components of the solution returned by ode45 to plot as a function of c (also returned by ode45). (If A and v are on the same scale, you could just do plot(c,z))
Your question is mainly about step 1. So write a function file
function dz = functionname(c,z)dz = zeros(size(z));% extract components of z (ie A & c)% define dz(1) according to the equation for dA/dc% define dz(2) according to the equation for dv/dc