dy/dx=（x+y）/（x-y）,求y=f（x）.
问题描述：
dy/dx=（x+y）/（x-y）,求y=f（x）.
答
dy/dx=(x+y)/(x-y),dy/dx=(1+y/x)/(1-y/x)u=y/x,dy/dx=u+xdu/dx(1+u)/(1-u)=u+xdu/dxdx/x=(1-u)du/(1+u^2)ln|x|=arctanu-(1/2)ln|1+u^2|+C(1/2)ln|x^2+y^2|-arctan(y/x)=C