求微分方程dy/dx=(x+y)/(x_y)的通解
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![求微分方程dy/dx=(x+y)/(x_y)的通解](/uploads/image/z/2622905-17-5.jpg?t=%E6%B1%82%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8Bdy%2Fdx%3D%28x%2By%29%2F%28x_y%29%E7%9A%84%E9%80%9A%E8%A7%A3)
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