求y''+2y'+y=e^-x/x的通解
问题描述：
求y''+2y'+y=e^-x/x的通解
y''+2y'+y=（e^-x）/x
答
p=dy/dx,y''=dp/dx=pdp/dypdp/dy+2p+y=0pdp/dy=-2pdp=-2dyp=-2y+cp=-2y+udp/dy=-2+u'(-2y+u)(-2+u')+2(-2y+u)+y=04y-2yu'-2u+uu'-4y+2u+y=02yu'=y2du=dyu=y/2p=-2y+y/2=-3y/2-3y/2*(-3/2)-3y+y=e^(-x)/xy=4e^(-x)/x