reset()
g=Graphics()
t = var('t')
C = function('C', t)
Q=1
V=3
k=0.33
cor=['black','red','blue']
def resolve(n):
   de=diff(C,t)==-k*C^n+Q*(1-C)/V
   f = desolve(de,[C,t], ics=[0,1])
   if len(f)<3:
      f=solve(f,C)[0].rhs()
   print "C(t)=",f
   return f

for i in range(3):
    f=resolve(i)
    g=g+plot(f,0,10, color=cor[i], legend_label="n=%s"%i)
g.axes_labels(['t', 'C(t)'])
g.show(dpi=90,ymin=0, title='Arranque de um CSTR') 

C(t)= 1/95957378424001*(959573784240*e^(1/3*t) + 94997804639761)*e^(-1/3*t)
C(t)= 1/199*(100*e^(199/300*t) + 99)*e^(-199/300*t)
C(t)= 10*(2*sqrt(31)*(199*e^(2/15*sqrt(31)*t) + 99) + 1985*e^(2/15*sqrt(31)*t) + 495)/(5960*sqrt(31)*e^(2/15*sqrt(31)*t) + 34601*e^(2/15*sqrt(31)*t) - 9801)