yy''-(y')^2-y'=0求微分通解
问题描述：
yy''-(y')^2-y'=0求微分通解
答
令y'=p,则y"=dp/dx=dp/dy·dy/dx=p·dp/dy所以原方程化为yp·dp/dy-p^2-p=0即p[y·dp/dy-(p+1)]=0所以p=0或y·dp/dy=p+1对于p=0,可解得y=(C1)；对于y·dp/dy=p+1,有y/py=(p+1)/dp=p/dp+1/dp即py/y=dp/(p+1)得lny=ln(...