I am not sure what method to use for the following ODE,


With $v=y'$, I got $$v'+y^{-1}v^2=y^{-1}e^{-y}v$$ and with $w=v^{-1}$,



$$y''+y^{-1}(y')^2=y^{-1}e^{-y}y'$$ $$yy''+(y')^2=e^{-y}y'$$ You have derivatives on both sides: $$(y'y)'=-(e^{-y})'$$ Integrate both sides.


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