Calculate duty cycle of flyback converter
However, I can't seem to find any way to find the
  \$\frac{N2}{N1}\$-ratio, when I only know the inductances of the
  coils.


This is likely to be what you are looking for: -

\$\dfrac{N_p}{N_s} = \sqrt{\dfrac{L_p}{L_s}}\$

The assumption for this is that both coils share the same magnetic core and are 100% coupled.