Hello all, since equations like this with x in front of f'(x) are pretty hard to solve so I came up with the idea (i don't know if this has a name) with guessing a solution for f(x) add c(x) and since there is a failure in my guess (otherwise I could solve it directly) I recalculate c(x). I add my calculation and if anyone of you is interested I would like to discuss it with you. I'm also not sure if there are any mistakes. It's just a hobby for me and it took me hours to solve this. So no exam pressure from my side (man I have to much time for this)!

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Here I am pointing out a slip you made. when I made one of my own! So sorry - my apologies.

e^[-ln(x)]is NOT -x but rather 1/x. Rookie error on my part.I have made the correction below - Ian