Is the function Lipschitz continuous on $ \overline{B_1(0)} $?

Question

$$ f(x,y)=\frac{2x^2y+y^3}{\sqrt{x^2+y^2}} $$ $$ I \ know \ that \ it \ is \ continuous \ on\ \overline{B_1(0)} \ . \\ I\ think \ I \ have \ to \ show \ ||f(x_1,x_2)-f(y_1,y_2)||\leq L||(x_1,x_2)-(y_1,y_2)|| \ , \ for \ x_i,y_i\in \overline{B_1(0)} \ ,\\i=1,2\ and \ L\in \mathbb{R}_+ $$