求方程dy/dx=(1+y^2)/(xy+yx^3)的解.

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dy/dx=(1+y^2)/[xy(1+x^2)]
y/(1+y^2)dy=dx/[x(1+x^2)]
2y/(1+y^2)dy=2xdx[x^2(1+x^2)]
d(y^2)/(1+y^2)=d(x^2)[1/x^2-1/(1+x^2)]
ln(1+y^2)=ln(x^2)-ln(1+x^2)+C1
1+y^2=Cx^2/(1+x^2)