求微分方程dy/dx=(x+y)/(x_y)的通解

求微分方程dy/dx=(x+y)/(x_y)的通解
求微分方程dy/dx=(x+y)/(x_y)的通解

求微分方程dy/dx=(x+y)/(x_y)的通解
dy/dx=(x+y)/(x-y)
x+y=u,x-y=t
y=(u-t)/2
x=(u+t)/2
dy/dx=(du+dt)/(du-dt)=u/t
udu-udt=tdu+tdt
udu-tdt=udt+tdu
d(u^2-t^2)=2dut
u^2-t^2=2ut+C
(x+y)^2-(x-y)^2=2(x+y)(x-y)+C
2x*2y=2(x^2-y^2)+C
2xy=(x^2-y^2)+C