find general solution of

xy(1+x^2)dy/dx-(1+y^2)=0

Solution:

this becomes

x(1+x^2) dy/dx=(1+y^2)/y

getting x's on one side and y's on the other

then the difficulties start, i tried to get the dy on the side of the y's to differenciate but when i do this i get 1/dy which seems weird

then tried

x(1+x^2) dy = (1/y+y) dx and differenciated left side(x's) with respect to y and the right side (y's) with respect to x which seems weird...

is this right?