I developed the following system of two ODEs while working on a problem of copulas:

f(u) (G(u) - G(0)) = 1,

g(v) (F(1) - F(v)) = 1

Here G is a primitive of g and F is a primitive of f.

I tried to solve the system via sage, which uses maxima for this, but maxima says it cannot solve the system. If that helps, one can assume that u and v belongs to the interval (0,1).