How do I solve the following differential equation: $$ f''(x)+\frac{(n-1)(f'(x))^2}{\sinh(x)}=0 $$ under the boundary conditions $f(1)=1$ and $\lim_{x\to\infty}f(x)=0$.
More generally, how to solve $$ f''(x)+g(x)(f'(x))^2=0 $$ for some known function $g(x)$ for the same boundary conditions.