The professor wrote the differential equation f²/f'=1 on the blackboard, and asked the students to solve it.

Everybody started working with the usual methods, except for a kid at the back of the class, who happened to have skipped that material, but was very bright.

Can you solve this equation without any integration?

(In reply to re(2): My (cryptic, mysterious, sibylline) Way by Old Original Oskar!)

Thanks for explaining.  I would assert that you did "integrate" the differential equation, as that is synonymous with "solve" in common parlance. However, your solution does not use definite integrals or even antiderivatives, and so can be described as integration-free.

It seems to me that the trick solution which tomarken gave is in contradiction to the problem statement in that the kid could not have been very bright to think that f²/f'=1 was supposed to be an algebraic equation with the ' being a 1, because  the exponent 1 is highly unlikely to be used in such a situation.

Thus, in my opinion, you are the winner here, Oskar!

Posted by Richard on 2006-05-02 17:16:01