I'm stuck in a classical mechanics problem. I have to solve this equation (actually I need only [tex]\ddot{x}[/tex]) to conclude it:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]x \frac{d^2x}{dt^2} + (\frac{dx}{dt})^2 -gx = 0[/tex]

The book offers a solution [tex]At^n[/tex] and it turns out that it's satisfied for n=2 and A=g/6 :surprised . Well, how am I supposed to guess that solution? It doesn't look Euler equation, or anything else I've seen before. Best I could do was to use brute force and expand it to series.

Question is, without this guesswork (and brute force), how can I solve/see it?

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# Nonlinear DE fro CM

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