求微分方程dy/dx=(x+y)/(x_y)的通解
问题描述：
求微分方程dy/dx=(x+y)/(x_y)的通解
答
dy/dx=(x+y)/(x-y)x+y=u,x-y=ty=(u-t)/2x=(u+t)/2dy/dx=(du+dt)/(du-dt)=u/tudu-udt=tdu+tdtudu-tdt=udt+tdud(u^2-t^2)=2dutu^2-t^2=2ut+C(x+y)^2-(x-y)^2=2(x+y)(x-y)+C2x*2y=2(x^2-y^2)+C2xy=(x^2-y^2)+C