Write Matlab function given an ODE and initial conditions

From this ODE

How do I write a Matlab program that calculates p at time 1.5 time units given a value of k3. I want to do a Matlab function that takes k3 as input and outputs p (1.5)?

Given the following s0 = 2.2, e0 = 2.8, k1 = 11 och k2 = 1.6.

With start values ​​s (0) = s0, e (0) = e0, c (0) = c0 = 0 and p (0) = p0 = 0

[Sara Westerlund]

I don´t want to use matlabs in built ODE solvers. Have used Eulers method before.

[Bjorn Gustavsson]

Why not? They are developed by experts in the field, that have gone to some considerable lengths to provide a suite of different solvers for ODEs with most types of numerical characteristics. If you know the shortcomings of these solvers for your type of ODE then you should also have sufficient competence to "roll your own" solver, but that doesn't fit very well with your "have used Euler's method before".

[Torsten]

Most probably, it's an assignment for which the OP has to program Euler's method.

Answer 1

[Bjorn Gustavsson]

Have a look at the ODE-examples, both the demos and the corresponding code:

>> odeexamples

That should give you a good starting introduction to how you should go about implementing your ODEs. Then you can also look at the help and documentation to ode45 and its siblings.

HTH