Why is rearranging 2x+y+xy'=3y²y' different ways giving inconsistent results?

[Ry122]

2x+y+(dy/dx)x=3y^2(dy/dx)
This is wrong:
(dy/dx)(x-3y^2)=-2x-y
This is right:
2x+y=(3y^2-x)(dy/dx)

Can someone please explain why.

 

[scottie_000]

This is wrong:
(dy/dx)(x-3y^2)=-2x-y
This is right:
2x+y=(3y^2-x)(dy/dx)

Those two equalities are actually the same, so I'm not sure "right" and "wrong" really apply.
The only difference is that the second is the negative of the first.
If you move each side of the first equality over the equals sign you will get the second

 

[Defennder]

Yeah, scottie_000 is right. Multiply the first by -1 and you'll get the second.

 

[Ry122]

So either answer would be correct in an exam?

 

[Defennder]

Of course, if they were strictly equivalent and your teachers don't mind.