Question

y=x乘y的导数加上y的导数的平方

Answer 1

是y=(xy)'+y'^2还是y=xy'+y'^2？

前者y=(xy)'+y'^2=y+xy'+y'^2 xy'+y'^2=0 x+y'=0 y'=-x y=(-x^2)/2 + c

后者y=xy'+y'^2 y'=y'+xy''+2y'y'' x+2y'=0 y'=-x/2 y=(-x^2)/4 + c