The discussion revolves around the manipulation of a differential equation involving variables x, y, and their derivatives. The original poster presents two forms of an equation and questions the validity of their equivalence.
Participants have engaged in a productive dialogue regarding the equivalence of the two expressions. Some have confirmed that both forms can be considered correct under certain conditions, while others are examining the implications of this equivalence in an academic context.
There is an underlying assumption about the acceptability of equivalent forms in educational settings, as well as a potential lack of clarity regarding the definitions of "right" and "wrong" in this context.
Ry122 said:This is wrong:
(dy/dx)(x-3y^2)=-2x-y
This is right:
2x+y=(3y^2-x)(dy/dx)