解微分方程y^2+(x^2)(dy/dx)=xy(dy/dx)
问题描述：
解微分方程y^2+(x^2)(dy/dx)=xy(dy/dx)
各路好汉小弟没财富了求帮帮忙,万谢!
答
y^2=(xy-x^2)dy/dx
y^2/x^2=(y/x-1)dy/dx
y/x=u
dy=udx+xdu
u^2=(u-1)(u-xdu/dx)
u^2/(u-1)=u-xdu/dx
xdu/dx=u-u^2/(u-1)
xdu/dx=-u/(u-1)
du/[u/(u-1)]=-dx/x
u-lnu=-lnx+C
y/x-ln(y/x)=-lnx+C