Putnam 2009 A2
Source:
December 7, 2009
Putnamfunctioncalculusderivativetrigonometrylogarithmsintegration
Problem Statement
Functions are differentiable on some open interval around and satisfy the equations and initial conditions
\begin{align*}f'&=2f^2gh+\frac1{gh},\ f(0)=1,\\
g'&=fg^2h+\frac4{fh},\ g(0)=1,\\
h'&=3fgh^2+\frac1{fg},\ h(0)=1.\end{align*}
Find an explicit formula for valid in some open interval around