Second Order Runge-Kutta Method for Problem

I am trying to generate a second order Runge Kutta method in matlab for the above problem and not sure where to start. Tried asking for help but was shown Mathematica code and example and I dont have Mathematica. Any help would be appreicated.

Answer 1

[Jeremy]

The ode solvers built into MATLAB are based on the runge-kutta method. Are you meant to implement your own method, or can you use ode23?

[David Geistlinger]

Can use existing method im just not sure how to use the runge kutta method in matlab

[Jeremy]

I would encourage you to read the documentation. Here is some syntax, if I read your problem correctly this should be the solution to the first part of your problem using ode23:

dxdt = @(t,x) 0.02 - 0.01*sqrt(x);
x0 = 0;
tspan = [0 600];
sol = ode23(dxdt,tspan,x0);
plot(sol.x,sol.y)

Also, please look at this:

doc ode23