I do not think the current API for dsolve when asking for series solution is done right. If one wants to obtain a series solution for an ODE, but wants different order than the default 6, now one must set this value using a global setting before making the call, like this:
It would be better if options to calls are passed along with the other parameters in the call itself. Something like
This should also apply to any command that takes Order, such as series(cos(x),x=0,order=10);
Passing options and values to functions using global and environment variables is not safe and not a good way to go about it as it can cause programming errors.