Then I am stuck. I think the provided answer contains an error. But even if they are right, why does this last step equal f(x,y) + g(y) ???

  • blind3rdeye@lemm.ee
    2·
    11 days ago

    I think they’re just being very sloppy with their definitions of the arbitrary functions f and g. In that if you integrate some arbitrary function, then you get some other arbitrary function - and they just used the same name. That’s my best guess for what they’re doing.

    Actually, there’s a whole lot about that ‘answer’ that I don’t like. I assume g(x) becoming g(y) is just a mistake. The implicit redefinition of the functions is bogus. And even if they were given new letters, I don’t like that the integration constants / functions are introduced before the integral is done. Like, I guess they are a result of integrating the LHS - but then we’re implicitly assuming that the other integral will give a constant of zero… To me that doesn’t look like good technique. But then again, maybe I’ve misunderstood the whole thing!

    • dysprosium@lemmy.dbzer0.comOP
      1·
      11 days ago

      Thx. Any idea where I can learn the right way that is clearer than this sloppy business? I basically threw in the towel of all courses since this hiccup

      • blind3rdeye@lemm.ee
        1·
        11 days ago

        Sorry, I’m not much help with that kind of advice. My knowledge about it mostly comes from dim memories of my time at university many years ago - with only some very minor bits being kept fresh by regular use.

        My only suggestion is that it would be good to use a reputable textbook, so that you can be fairly confident that it is correct and not cutting corners; and then when you practice yourself, you should also make a conscious effort to not cut corners. (It’s always tempting to just fudge any changes to arbitrary constants as being unimportant - since they are still arbitrary constants anyway; and mostly it doesn’t matter. But that’s a bad habit, because sometimes it does matter, and won’t notice those times unless you’ve been paying attention all the time.) I won’t try to recommend specific sources though, because I’m very out-of-date with that. I’ll just say that published books used by universities are likely to be better than the notes of a private tutor or small online course.