e^y + xy - e = 0,求y’’表达式
问题描述：
e^y + xy - e = 0,求y’’表达式
答
方程两边对x求导,y看成是x的函数e^y×y'+y+xy'-0=0(x+e^y)y'=-yy'=-y/(x+e^y)两边再同时对x求导,y看成是x的函数y"=[y(1+e^y y')-y'(x+e^y)]/(x+e^y)²=[y+(ye^y-x-e^y)y']/(x+e^y)²把 y'=-y/(x+e^y)代入上...能消去Y吗？这里y是消不去的, 要看成是x的函数来求导 对不起, 把 y'=-y/(x+e^y)代入上式y"=[y+(ye^y-x-e^y)y']/(x+e^y)², 最终结果是 y"=[2xy+(2y-y²)e^y]/(x+e^y)³