Question

求dy y=y(x)是由方程y=1+xe^y所确定函数,求dy

Answer 1

y=1+xe^y

两边求导

y'=e^y+y'*xe^y

∴y'-y'*xe^y=e^y

∴y'(1-xe^y)=e^y

∴dy=y'dx=e^ydx/(1-xe^y)