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?

Ya know, I realize that there are a few different solutions to the differential equation because of the fact that the domain isn't specified. For each C in the discussed family of solutions, we are actually over a different domain. If I am granted the ability to throw out a finite number of reals instead of just one, we can use a different C over different intervals. This would allow the construction of convex solutions and bounded solutions defined almost everywhere.

Or I may be having a momentary mind melt :-)

Posted by owl on 2006-05-03 11:38:22