Question

Find `dy/dx` if x³ + y³ = 3axy

Answer 1

Given: x³ + y³ = 3axy

Differentiating w.r.t. x, we get

`3x^2 + 3y^2 dy/dx = 3a (1.y + x dy/dx)`

⇒ `x^2 + y^2 dy/dx = ay + ax dy/dx`

⇒ `dy/dx (y^2 - ax) = ay - x^2`

⇒ `dy/dx = (ay - x^2)/(y^2 - ax)`