Solving ODEs: The Frobenius Method, worked examples

ordinary-differential-equations

but my powers stop there. Can I multiply the two series together? I would have to multiply each term in one series by every term in the other, and I don't know how to deal with that.

I cracked my head about that a little while and I figured out how you can multiply two infinite series without getting lost. Here's an animation explaining my technique:

enter image description here

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