I have a system of two nonlinear ODEs with initial conditions. Mathematica's DSolve is unable to produce something. NDSolve gives a plot of two strictly decreasing nonlinear functions from numerically solving this. However I am looking for an analytical solution.
$g'(x)=\frac{g(x)}{1.25-x-h(x)}$
$h'(x)=\frac{h(x)}{1.75-x-g(x)}$
with $g(1)=1$ and $h(1)=1$.