The prime notation is not working on my keyboard yet.

restart;

with(student):

interface(typesetting = extended);

Typesetting:-Settings(typesetprime = true);

and  are not working on my keyboard as prime?

int((10000*k/(100*k*P(t) - 1) - 100/P(t))*diff(P(t), t), t = 0 .. t) = t;

P(t)=solve(%,P(t));

Error, (in solve) cannot solve expressions with diff(P(t), t) for P(t)

Applications to Differential Equations