Using ode45 To Solve a System of 2nd Order ODEs

I have the following set of 2 Second Order ODEs:

I need to solve these equations simultaneously, so that in the first equation is used in in the second equation.

I'm looking everywhere for the solution of my problem, but no luck.

I know from https://www.mathworks.com/help/matlab/math/choose-an-ode-solver.html that I need to transform a 2nd Order ODE in a 1st Order ODE, but how to do it with 2 ODEs and in an iterative way?

Can someone help me to use ode45 for this problem?

Thank you,

Rafael F.

Answer 1

[Star Strider]

Code them in the Symbolic Math Toolbox, and use the functions odeToVectorField and then matlabFunction to create an anonymous function that the ODE solvers such as ode45 can use to integrate them. There are other differential equation functions in the Symbolic Math Toolbox Mathematics documentation section if these turn out not to be appropriate for your system.

[Rafael Fehér]

Thank you, Mr. Strider. Using odeToVectorField and matlabFunction, I was able to solve que system of 2nd Order EDOs.

[Star Strider]

As always, my pleasure!