How to solve this system of differential equations in matlab?

Question

My task is to model a certain physical problem and use matlab to solve it's differential equations. I made the model but it seems far more complex than what I've learned so far so I have no idea how to solve this.

The black color means it's a constant

Answer 1

I assume that by "solve" you seek a closed form solution of the form x(t) = ..., z(t) = ... Unforunately, it's very likely you cannot solve this system of differential equations. Only very specific canonical systems actually have a closed-form solution, and they are the most simple (few terms and dependent variables). See Wikipedia's entry for Ordinary Differential Equations , in particular the section Summary of exact solutions .

Nevertheless, the procedure for attempting to solve with Matlab's Symbolic Math Toolbox is described here .

If instead you were asking for numerical integration , then I will give you some pointers, but you must carry out the math:

1. Convert the second order system to a first order system by using a substitution w(t) = dx/dt, allowing you to replace the d2x/dt2 term by dw/dt. Example here.

2. Read the documentation for ode15i and implement your transformed model as an implicit differential equation system.

NB You must supply numerical values for your constants.