dy/dx=y/x+y/xln(y/x)
令y/x=u
y=ux
dy/dx=u+xdu/dx
u+xdu/dx=u+ulnu
xdu/dx=ulnu
1/ulnu du=1/xdx
两边积分,得
∫1/lnu dlnu=∫dlnx
ln|lnu|=lnx+lnc1
lnu=c1x
u=e^c1x
dy/dx=e^c1x
y=1/c1 e^c1x+c2