2y=-1+xy^3

2y=-1+xy^3

2y'=(xy^3)'=y^3+x(y^3)'=y^3+3xy^2*y'

(2-3xy^2)y'=y^3

y'=y^3/[2-3xy^2]

2y=-1+xy^3 两边同时求导
2dy=y^3dx+x*3y^2dy
所以导数y'=dy/dx=(2-3xy^2)/y^3

大学数学解题法诠释
编者:徐利治
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