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?

I don't know know what "without integration" is supposed to mean in this context, but f'/f²=1 is the same as -(1/f)'=1 so -1/f=x+c and thus f=-1/(x+c).  Was there integration there or not?

Posted by Richard on 2006-05-02 14:08:20