A note about series solutions of Differential Equations in MATLAB

MATLAB releases through 2019b do not include a command for computing
series solutions to differential equations.  However, there is such
a command, ode::series, in MuPAD.  Thus there are three ways
to find the series solution to a differential equation (out to a specified
order). The first two of these are either to open a MuPAD notebook and do 
the calculation there, or else to use the command evalin to access the 
command ode::series and send the result back to the MATLAB Workspace.  
You can see this second method illustrated in the accompanying 
live script seriessol.mlx. The final method is to avoid the
direct MuPAD commands altogther and just program the algorithm of
solving recursively for the coefficients.  This is illustrated
in the live script seriessol1.mlx. Or one could work in the command
window using the function file seriessolve.m. Download the function
file and type help seriessolve for the syntax.

If you have MATLAB release 2020a or later, then series solutions
can be computed directly using an option to the dsolve command.
See the link marked Series on the index page for this folder,
or else go directly to https://schol.math.umd.edu/ode/dewmtlb_series.html