y-xe^y=2确定的函数为y=y(x),求y"
问题描述：
y-xe^y=2确定的函数为y=y(x),求y"
答
y-xe^y=2y'-e^y-xe^y*y'=0y'(1-xe^y)=e^y 1y'=e^y/(1-xe^y)对1式再次求导得y''(1-xe^y)+y'(-e^y-xe^y*y')=e^y*y'y''(1-xe^y)=e^y*y'+e^yy'+xe^y(y')^2=2e^y*y'+xe^y(y')^2=e^y(2y'+(y')^2)=e^y(2e^y/(1-xe^y)+(e^y/(...