Hi everyone

I am an engineering student and I am having a little difficulty with a bit of exam practice involving solving an ODE with Runge-Kutta. I am able to use both in most examples, but this one is a little different.

Any help you can give me would be amazing, so thanks for anything you can help me with!

The Question:

over the interval

and with the boundary conditions

I have solved by using an auxhilary equation already, as outlined in the first part of the equation.

The second part of the equation is where I have the trouble with:

"For a system of first order equations on

with initial conditions

and

, deruve the second order Runge-Kutta method based on using the trapezium rule to give approximations

and

to

and

for

"

I have devised two first order ODE's:

and

I think these are correct, but I am unsure on how to use them correctly. Every example we have from class is using a two variable function and I cannot find anything on the internet about it ( maybe using the wrong names ).

I look forward to what you guys have to say, cheers guys.