y = 1+xe^y...........................................(1)
y' = e^y + xy' e^y..................................(2)
y' = e^y/(1-xe^y)...................................(3)
(2) 式再对x求一次导数:
y'' = y'e^y + y'e^y + xy''e^y + xy'^2e^y
解出:
y'' = y'(2+xy')e^y / (1+xe^y)..................(4)
将(3) y‘ 代入(4) ,整理后即为所求。