(1+2e^(y/x))dx+(2e^(x/y))*(1-x/y)dy=0

（1+2e^x/y)dx+2e^x/y(1-x/y)dy=0,令x/y=v,则得dx/dy=ydu/dy+u,代入得u+ydu/dy
=-2e^u(1-u)/(1+2e^u),移项并通分得ydu/dy=-(2e^u-u)/1
+2e^u,即du(1+2e^u)/-2e^u-u=dy/y.即-ln(2e^u+u
)=ln(y)+c,所以得2ye^x/y+x=c

(1+2e^(y/x))dx+(2e^(x/y))*(1-x/y)dy=0(1+2e^(y/x))dx+(2e^(x/y))*(1-x/y)dy=0(1+2e^(y/x))dx+(2e^(x/y))*(1-x/y)dy=0(1+2e^(y/x))dx+(2e^(x/y))*(1-x/y)dy=0(1+2e^(y/x))dx+(2e^(x/y))*(1-x/y)dy=0(1+2e^(y/x))dx+(2e^(x/y))*(1-x/y)dy=0(1+2e^(y/x))dx+(2e^(x/y))*(1-x/y)dy=0(1+2e^(y/x))dx+(2e^(x/y))*(1-x/y)dy=0(1+2e^(y/x))dx+(2e^(x/y))*(1-x/y)dy=0(1+2e^(y/x))dx+(2e^(x/y))*(1-x/y)dy=0(1+2e^(y/x))dx+(2e^(x/y))*(1-x/y)dy=0(1+2e^(y/x))dx+(2e^(x/y))*(1-x/y)dy=0(1+2e^(y/x))dx+(2e^(x/y))*(1-x/y)dy=0(1+2e^(y/x))dx+(2e^(x/y))*(1-x/y)dy=0(1+2e^(y/x))dx+(2e^(x/y))*(1-x/y)dy=0(1+2e^(y/x))dx+(2e^(x/y))*(1-x/y)dy=0(1+2e^(y/x))dx+(2e^(x/y))*(1-x/y)dy=0(1+2e^(y/x))dx+(2e^(x/y))*(1-x/y)dy=0(1+2e^(y/x))dx+(2e^(x/y))*(1-x/y)dy=0(1+2e^(y/x))dx+(2e^(x/y))*(1-x/y)dy=0(1+2e^(y/x))dx+(2e^(x/y))*(1-x/y)dy=0(1+2e^(y/x))dx+(2e