I got the next DE on a lesson 2 weeks ago. After I wasn't able to find any solution my teacher assigned it to be my homework. Thrice. Last time on a lecture he said it will be my prerequisite for exam (not quite sure if it's in conflict with forum rules...). But because of it being my homework three times I can't hand over any other homework and I lose opportunities for activity points... That 'simple' DE is:
The facts are:
(1)Simple techniques we've learnt up to now doesn't seem to work. I am unable to efficiently separate variables, the substitution leads to probably unsolvable(?) integral. Also I should mention that we started this DE topic on lectures only recently.
(2)I groped a bit in an accessible literature recommended by teacher and luckily I figured out where does the DE comes from (Elias J., Horvath J., Kajan J.,- Zbierka uloh z vyssej matematiky). It's a problem no.1194, but result listed at the end of the book isn't correct ( ). Neither problem no.1193 nor no.1195 have correctly listed solutions, but the former one matches correct result for problem no.1193. Given solutions at the end slightly resemble those correct ones, like if they were incorrectly rewritten from somewhere else...
(3)Wolfram can't solve neither that DE nor the derived integral.
(4)On the last lesson I told my teacher the book has incorrect results and that my DE possibly can't be solved but he insisted on it can be done. So now it's my homework for a third time
Because it's my homework I just ask for hints what technique of DE-solving should I use, not the entire flat solution... Also it would be of great appeasment to me if anyone could confirm it can be really solved.
Now make the substitution
and the integral becomes
I'm afraid I don't know how to continue...