I'm trying to see why my textbook's solution is correct and mine isn't.
"Find an expression in terms of $x$ and $y$ for $\displaystyle \frac{dy}{dx}$, given that $x^2+6x-8y+5y^2=13$
First, the textbook's solution, which I understand and agree with fully:
Now my similar solution, for which I don't see my error:
Differential: $2x+6-8\frac{dy}{dx}+10y\frac{dy}{dx}=0$ $\frac{dy}{dx}(10y-8)=-2x-6$ $\frac{dy}{dx}=\frac{-2x-6}{10y-8}=\frac{-x-3}{5y-4}$
So I end up with the negative of the correct solution, because I moved the $(2x+6)$ to the RHS and the textbook author moved the other part instead. I would have thought it would produce an equivalent answer?
Thanks!