hey, can someone explain to me how mathematicians found out that for second order homogenous ODEs with constant coefficents, when for the auxiliary equation, b^2 - 4ac = 0, xe^(rx) is another general solution?(adsbygoogle = window.adsbygoogle || []).push({});

I've seen it proven, but I don't understand why

**EDIT:*** I just realized I may have phrased this in an awkward/weird way. In other words, how did they find out that it works? I mean, I know when you plug it in to the regular equation, it works, but there must be something more to it (at least that's what I imagine, I could very well be wrong though).

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# Y1 = xe^(rx) and y2 = e^(rx): how y1 was discovered?

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