求xy''-y'+xy'^2=0的通解
问题描述：
求xy''-y'+xy'^2=0的通解
答
令x=e^t,则xy'=dy/dt,x²y''=d²y/dt²-dt/dt于是,代入原方程得d²y/dt²-2dy/dt+(dy/dt)²=0.(1)再令dy/dt=p,则d²y/dt²=dp/dt于是,代入方程(1)得dp/dt-2p+p²=0==>dp/(p(2-p...