直接分离变量：ydy/(1+y²)=xdx/(1+x²)d(y²)/(1+y²)=d(x²)/(1+x²)积分：ln(1+y²)=ln(1+x²)+C11+y²=C(1+x²)代入y(0)=1,得：1+1=C,得C=2故特解为1+y²=2(1+x²)即y²-2x²=1
