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I came across this question Nonlinear PDE $u_y=(u_x)^3$ but upon reading it I noticed what as far as I know is a mistake.

For a general first equation of the form $F(x,y,z,u_x,u_y)=0,$ one of the characteristic strips should be $\frac{du}{ds} = pF_p + qF_q$. Therefore when this person is using the Lagrange-Charpit equations, they should actually have $\frac{dy}{-1}=\frac{du}{3p^3-q}$ since $qF_q = q(-1).$ So what am either I or this other person doing wrong?

Bangarang
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  • Wow nothing huh? That's kind of surprising. – Bangarang Mar 08 '20 at 18:19
  • Of course everybody see that there is a typo in the equation which should be : $$\frac{\mathrm{d}x }{3p^2} = \frac{\mathrm{d} y}{-1} = \frac{\mathrm{d}u }{3p^3-q} = -\frac{\mathrm{d} p}{0} = -\frac{\mathrm{d} q}{0}.$$ The further calculus and final result is correct. Why did you open a new question about a typo? It is simpler to simply correct it. – JJacquelin Mar 09 '20 at 06:33
  • Stackexchange self-proclaims its expertise by the expectation that a reputable person would have already corrected such a mistake after 6 years. Instead of being arrogant, which is apparently the norm here judging by your comment, I open-mindedly asked a question about it rather than making a careless assumption. I highly doubt this site would want random people arbitrarily modifying random questions. – Bangarang Mar 09 '20 at 06:54
  • When a typo is observed it is of use to point it out in the comments section, not to open a new answer about the typo. The correction of the typo by someone else than the author itself is accepted or rejected by reviewers through "Review queues". – JJacquelin Mar 09 '20 at 08:35
  • Except one generally needs an high reputation to do so. This is nearly always the case for old questions, and the restriction is even higher for popular questions. – Bangarang Mar 09 '20 at 08:38
  • Thanks to you the typo in Dmoreno's answer to https://math.stackexchange.com/questions/903659/nonlinear-pde-u-y-u-x3 was corrected. Nobody disputes the usefulness of your comment. But it should be better to delete your question and post your comment in the comments section of the original topic. – JJacquelin Mar 09 '20 at 09:10
  • We just went over this. The site does not let new members post anything on these older posts. Older posts are always locked that way. and popular older posts are even worse. In some ways this makes sense, but don't complain that I can't do something that your site decided I can't do. – Bangarang Mar 09 '20 at 16:38
  • I’m voting to close this question because the mistake in the answer mentioned by the OP was corrected. – Gonçalo Feb 14 '24 at 07:20

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