求积分,dy/dx=(x-y-1)/(x+y+1)
问题描述：
求积分,dy/dx=(x-y-1)/(x+y+1)
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方程变为dY/dX=(X-Y)/(X+Y),令u=(Y/X),代入,得(1+u)du/(1-2u-u^2)=-dX/X,积分得1-2u-u^2=Cx^2.
我不懂：u=(Y/X),代入,得(1+u)du/(1-2u-u^2)=-dX/dX,具体怎么代入得到?
答
y=ux,dy=udx+xdu,dy/dx=u+xdu/dx=(1-u)/(1+u),xdu/dx=(1-2u-u^2)/(1+u),还有不懂吗
把y=ux两边微分就可以了