Implicit physics question

1. Nov 23, 2004

Tom McCurdy

taking derivitive of 2xy^2+xy=y

split up to using product rule

$$2x----2$$
$$y^2---2y\frac{dy}{dx}$$

$$4yx\frac{dy}{dx}+2y^2+y+x\frac{dy}{dx}=\frac{dy}{dx}$$

$$\frac{dy}{dx} (4x+x-1)=-2y^2-y$$

$$\frac{dy}{dx}= \frac{-2y^2-y}{4xy+x-1}$$

i am trying to figure out the slope of the equation when y-1

am i doing all this for nothing?

Last edited: Nov 23, 2004
2. Nov 23, 2004

Falnom

Do you mean when y=1?
If so then all you have to do is plug back in y in the orignal equation and solve for x. And then plug in both x and y into your final differential equation. I think that the final slope will then be -9/2.