dy/dx=(x^3+y^3)/xy^2
(x^3+y^3)/xy^2=f(y/x)
y=t(x)x
y'=xt'+t
(x^3+(tx)^3)/ (x(tx)^2)=xt'+t
(x^3+t^3x^3)/(xt^2x^2)=xt'+t
(1+t^3)/t^2=xt'+t
1/t^2+t=xt'+t
xt'=1/t^2
t^2dt=dx/x
t^3=ln |x|+c
(y/x)^3=ln|x|+c
(y^3-x^3ln|x| )/x^3=c
dy/dx=(x^3+y^3)/xy^2
(x^3+y^3)/xy^2=f(y/x)
y=t(x)x
y'=xt'+t
(x^3+(tx)^3)/ (x(tx)^2)=xt'+t
(x^3+t^3x^3)/(xt^2x^2)=xt'+t
(1+t^3)/t^2=xt'+t
1/t^2+t=xt'+t
xt'=1/t^2
t^2dt=dx/x
t^3=ln |x|+c
(y/x)^3=ln|x|+c
(y^3-x^3ln|x| )/x^3=c