Thank you all for your help. I appreciate your help a lot. Although, I have now some output, I am not really sure what I/you are doing.
Concerning Doug Meade his solution: I understand what you try. However my question was not to >plot (ETa, Pna=0..100) but to >plot(ETa, Pa=0..100). Plotting >plot(ETa, Pna=0..100) was already possible with >plot(evalf(ETa),Pna-0..100). That works quite fast. The assumption that Pna>0 is indeed correct. What is the line >value(ETa2) doing?
Concerning the solution of Robert Israel: What are you doing by >Intb:=PDEtools[dchange](Pm=1/u-1,Inta,u); ?? What I now did is
>ETa := value(convert(ETa,piecewise)) assuming Pna > 0;
and that's seems to work (also fast). Also the solution looks understandable for me. However for you the same question as for Doug. What do you do with the first line? Why is this necessary? Only to make it quicker?
Anyway, thanks a lot for your answers!!!