Functions f,g,h are differentiable on some open interval around 0 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 f(x), valid in some open interval around 0. Putnamfunctioncalculusderivativetrigonometrylogarithmsintegration