∵dz/dx+z/x=-3lnx
==>xdz/+zdx=-3xlnxdx
==>d(xz)=d(3x^2(1-2lnx)/4)
==>xz=3x^2(1-2lnx)/4+C (C是常数)
==>z=3x(1-2lnx)/4+C/x
∴原方程的通解是z=3x(1-2lnx)/4+C/x.