[superfsy]

input:=Clear[s, g, t, c0, k];
DSolve[{-s'[g] == k s[g]/(1 - g), s[0] == s0}, s[g], g]
output:={{s[g] -> (-1)^-k (-1 + g)^k s0}}

实际用分离变量手动计算的话解应该是：
s[g]=s0(1-g)^k

请达人指教！