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I have a problem with Mathematica, When I solve this equation in Mathematica and also in wolframalpha I have different solutions [enter image description here[1]enter image description here

a'[t]^2 - A a[t] a'[t] - B a[t]^2 + F = 0

DSolve[y'[x]^2 - A y[x] y'[x] - B y[x]^2 + F == 0, y, x]

Log(F - B a^2) vs Log(B a^2 - F) ??!!

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    $\begingroup$ People here generally like users to post code as Mathematica code instead of just images or TeX, so they can copy-paste it. It makes it convenient for them and more likely you will get someone to help you. You may find the meta Q&A, How to copy code from Mathematica so it looks good on this site, helpful $\endgroup$
    – Michael E2
    Sep 28, 2021 at 16:05
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    $\begingroup$ Log(F-B a^2) and Log(B a^2-F) differ by a constant. Maybe it doesn't matter? $\endgroup$
    – Michael E2
    Sep 28, 2021 at 16:05
  • $\begingroup$ the difference is the negative sign! Michael E2 $\endgroup$
    – Mathecis
    Sep 28, 2021 at 17:29
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    $\begingroup$ Yes, exactly. If it's the last term in the W|A output that you are pointing out, then the difference of a constant $i\pi$ does not matter because of the arbitrary constant $c_1$ on the other side of the equation. (If you mean some other term, I don't know what it is.) $\endgroup$
    – Michael E2
    Sep 28, 2021 at 17:33
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    $\begingroup$ Please make sure that code is contained in code blocks (for readability), and state your question explicitly. There is no explicit question in this post. Please also edit the tags, and use only relevant ones. Is your question related to plotting in any way? To exporting data? $\endgroup$
    – Szabolcs
    Sep 28, 2021 at 17:44

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