If `x^3+y^3=3a x y` , find `(dy)/(dx)`

Explanation

Given, `x^{2}+y^{3}=3` axy...(1)



Differentiating equation,
$$ \Rightarrow 3 x^{2}+3 y^{2} \frac{d y}{d x}=3 a\left(x \frac{d y}{d x}+y\right) $$
$$
\Rightarrow 3 x^{2}+3 y^{2} \frac{d y}{d x}=3 a x \frac{d y}{d x}+3 a y
...