Can I create a matrix of differential operators?

Hi everyone, I'm new here but I've been familiar with the basics of Matlab for quite a while.

I want to know if it is possible to create a differential operator in a matrix. The reason is that the research I'm doing regarding vibrations; involves some very lengthy differential equations in which the variables can change quite drastically depending on the boundary conditions of the problem. Most of the time the analysis on particular boundary conditions require me to write out different forms of the matrix that are pre-determined (obtained from textbooks etc.) which isn't very robust.

There are 3 homogeneous ODE's that each incorporate the displacement/time functions u(x,theta,t) , v(x,theta,t) and w(x,theta,t). If I put these in a matrix B=[u,v,w], I could output the 3 ODEs by multiplying the differential operator by B. So AB=0. So basically each column will be for u,v and w. This will allow me to determine the coefficients of the general solutions for u,v and w. I already know what the matrix 'A' is, but I'm not sure how to actually implement it in Matlab to obtain what I've described.

Any help would be greatly appreaciated. Thank you.

Answer 1

[Walter Roberson]

The symbolic toolbox has support for differential operators and solving ODEs. I believe the appropriate command is dsolve()