ALWAYS to answer your question, refer to the "MIDI IMPLEMENTATION CHART" for your MIDI instrument.
This chart can be found USUALLY near the end of your user's manual.
This chart, among other things, will tell what can be transmitted and received by the MIDI device.
Refering to the chart for your DX21 it shows that the DX21 can both receive and transmit program changes.
If you don't have a user manual, download one here:
http://www.maths.abdn.ac.uk/~bensondj/dx7/manuals/dx21-man.pdf
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