1st Putnam 1938 Problem B2 Find all solutions of the differential equation zz" - 2z'z' = 0 which pass through the point x=1, z=1. Solution
: z = 1/( A(x - 1) + 1). We have z''/z' = 2 z'/z. Integrating, ln z' = 2 ln z + const, so z' = - A/z 2 . Integrating again: 1/z = Ax + B. But z(1) = 1, so B = 1 - A. 1st Putnam 1938 © John Scholes jscholes@kalva.demon.co.uk 5 Mar 2002