Answer to Question #320380 in Calculus for koi

Question

Find 𝑑𝑦 𝑑𝑥 if 𝑥 2𝑦 + 2𝑦 3 = 3𝑥 + 2𝑦

Answer 1

$x²y+2y³=3x+2y$

$2xy+x²\frac{dy}{dx}+6y²\frac{dy}{dx}=3+2\frac{dy}{dx}$

$x²\frac{dy}{dx}+6y²\frac{dy}{dx}-2\frac{dy}{dx}=-2xy+3$

$(x²+6y²-2)\frac{dy}{dx}=3-2xy$

$\frac{dy}{dx}=\frac{3-2xy}{x²+6y²-2}$