该微分方程能够分离变量。xy'+1=4e^(-y)(dy/dx)x=(4-e^y)/e^y[e^y/(e^y-4)]dy=(-1/x)dxln(e^y -4)=-lnx +C=ln(e^C /x)e^y=(4x+e^C)/x得通解：y=ln[(4x+e^C)/x]
