\(\displaystyle

s''(z)-s'(z) +s(z) =e^{-2z}s(z)s'^2 (z)

\).

maybe \(\displaystyle s=p(z)e^z \) will reduce the equation into an easier one , \(\displaystyle \; [p'e^z + e^z p ]'-p'e^z =e^{-2z} pe^{z} s'^2 (z)=e^{z}p [p'+p]^{2}\).

\(\displaystyle p'e^z +p''e^z +e^z p =e^{z}p [p'+p] \; \) ; \(\displaystyle \; p''+p'=pp'+p^2 \).

\(\displaystyle [p'+p]'=p[p'+p] \; \) , how to continue from here ?