#F(x,y)=2 (x^2 + y^2)/x - 3 (x^2 - y^2)/y = 0# is an homogeneous function so susbtituting #y = lambda x# we obtain
#F(x, lambda x) = (x (-3 + 2 lambda+ 3 lambda^2 + 2lambda^3))/lambda = 0# with one real solution which is
#lambda =
1/2 ((63 + 2 sqrt[993])^(1/3)/3^(2/3) -
1/(3 (63 + 2 sqrt[993]))^(1/3)-1)#
discarding #x=0,lambda=0# and considering only real values for #lambda#.
#lambda =0.6359991#.
#F(x,y)=0 equiv y = 0.6359991 x#
so #dy/dx = 0.6359991#