x(1+y^2)+y(1+x^2)dy/dx=0 尤其是积分的步骤请详细讲解

题目

x(1+y^2)+y(1+x^2)dy/dx=0 尤其是积分的步骤请详细讲解

答案

x(1+y^2)+y(1+x^2)dy/dx=0x(1+y^2)=-y(1+x^2)dy/dxy/(1+y²)dy=-x/(1+x²)dx2y/(1+y²)dy=-2x/(1+x²)dx1/(1+y²)dy²=-1/(1+x²)dx²两边同时积分,得ln(1+y²)=-ln(1+x²)...