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## Main Question or Discussion Point

We know that there are a few forms for 1st order differential equations. Second-order differential equations have an extra term with an [itex]x[/itex] in it. My conjecture is that third-order differential equations have

Thanks in advance! :)

*another*extra term with an [itex]x^2[/itex] in it. A friend of mine agrees with this. Is this true and can we following the same pattern for higher order differential equations? If so, is there a proof to this?Thanks in advance! :)