Below are the graphs for an example done in class on Friday, Aug. 24.

> with(plots):

> with(DEtools):

> dfieldplot(diff(y(x),x)+y(x)/(x-1)=1/(x-3), y(x), x=0..5,y=-5..5,color=black,thickness=2,arrows=line);

> plot((x+ln((x-3)^2)-2)/(x-1),x=0..5,y=-5..5,discont=true,thickness=2);

> df:=dfieldplot(diff(y(x),x)+y(x)/(x-1)=1/(x-3), y(x), x=0..5,y=-5..5,color=black,thickness=2,arrows=line):

> sol1:=plot((x+ln((x-3)^2)-2)/(x-1),x=1..3,y=-5..5,discont=true,thickness=2,color=red):

> sol2:=plot((x+ln((x-3)^2)-3)/(x-1),x=1..3,y=-5..5,discont=true,thickness=2,color=blue):

> sol3:=plot((x+ln((x-3)^2)-(ln(4)+1))/(x-1),x=1..3,y=-5..5,discont=true,thickness=2,color=green):

> display(df,sol1,sol2,sol3);