He succeeded in characterising those differential equations the solutions of which have no essential singularity in the extended complex plane. Fuchs later also studied non-linear fifferential equations and moveable singularities.
Tagumpay siya sa characterising mga kaugalian ang equation na solusyon ng walang mahahalagang katangian sa extended kumplikadong eroplano. Fuchs mamaya din-aral ng mga di-guhit fifferential equation at naigagalaw singularities.