Question

find dy/dx implicitly and explicitly and then prove that they are equal.
xy + ay -a+x=0
Please, help

Answer 1

explicitly:
y(x+a) = a-x
\(y =\dfrac{a-x}{a+x}\)
then \(\dfrac{dy}{dx}= -(a+x)-(a-x)}{(a+x)^2}=\dfrac{-2a}{(a+x)^2}\)

Answer 2

Any mistake?

Answer 3

Implicitly:
y +xy' +ay' +1=0
\(dfrac{dy}{dx}=\dfrac{-1-y}{x+a}\)
oh, I think I find out my mistake.
Sorry for bothering. :)

Answer 4

correct