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: Observations and maybe solution by Federico Kereki)

My own view was that I took an antiderivative, which is not the same thing as integrating.  Also, solving a differential equation is commonly known as integrating it.  Nevertheless, it seems you have something else in mind, and I will just be patient and hope to find out what that is before too long.  I don't see how there can be any simpler solution process than the one I gave, however, so I don't  see how a non-integration approach can be the answer to a maiden's prayer, so to speak.

Posted by Richard on 2006-05-02 15:52:45