Question

Find $\frac{dy}{dx}$

if $(x^2+y^2{)}^2=xy$ ?

Answer 1

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

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

$4x^3+4x^{2}y\frac{dy}{dx}+4x{y}^2+4y^3\frac{dy}{dx}=(x\frac{dy}{dx}+y)$

$(4x^{2}y+4y^3-x)\frac{dy}{dx}=y-4x^3-4x{y}^2$

$\frac{dy}{dx}=\frac{(y-4x^3-4x{y}^2)}{(4x^{2}y+4y^3-x)}$