解微分方程 y*y''-(y')^2-y^2*y'=0
问题描述：
解微分方程 y*y''-(y')^2-y^2*y'=0
答
yy''-y'^2=y^2y'
(yy''-y'^2)/y^2=y'
(y'/y)'=y'
两边积分：y'/y=y+C1
dy/dx=y^2+C1y
dy/[y(y+C1)]=dx
两边积分,
左边=1/C1∫(1/y-1/(y+C1))dy=1/C1ln|y/(y+C1)|+C2
右边=x+C2
所以1/C1ln|y/(y+C1)|=x+C2
ln|y/(y+C1)|=C1x+C2
y/(y+C1)=C2e^(C1x)
y=C1C2e^(C1x)/(1-C2e^(C1x))