There is a following example in one of the 18.01 lectures:

y^4 + xy^2 - 2 = 0
y' = -y^2 / (4y^3 + 2xy)

What is the reason that y does not get cancelled?

Question

There is a following example in one of the 18.01 lectures:

y^4 + xy^2 - 2 = 0
y' = -y^2 / (4y^3 + 2xy)

What is the reason that y does not get cancelled?

.sam. · Answer

$$4y^3\frac{dy}{dx}+(2xy\frac{dy}{dx}+y^2)=0 $$
$$\frac{dy}{dx}(4y^3+2xy)+y^2=0$$
$$y'=\frac{-y^2}{4y^3+2xy}$$

anonymous · Answer

Ye, hence the question why we are not cancelling one of the "y" in the right hand side.

.sam. · Answer

Oh you can cancel

.sam. · Answer

there's nothing wrong but leaving this form is the same

anonymous · Answer

because if they canel and when intergrating it,it is not going to give you the original equestion

.sam. · Answer

Its the same

anonymous · Answer

Thanks, that's what I thought initially. Just felt weird that no one asked this at the lecture, like I was missing something obvious.