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?

Answer 1

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

Answer 2

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

Answer 3

Oh you can cancel

Answer 4

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

Answer 5

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

Answer 6

Its the same

Answer 7

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