Wolfram Mathematica Plot Differential Equations System

Question

I want to see what it will happen for different values of the parameters k1 and k2, but all I have is an empty graphics. Can someone help me?

Manipulate[
  Plot[
    { x -> Function[ {t}, 
        1 - (-1 + k2*E^(k1*t + k1 )) / (-1 + k1*E^(k1*t + k1 ) + 
          k2*E^(k1*t + k1 )) ], 
      u -> Function[ {t}, 
        (-1 + k2*E^(k1*t + k1) ) / (-1 + E^(k1* t + k1 ) *k1 + 
          E^(k1 t C[1] + k1 C[1] C[2])*k2) ] }, 
    { t, 0, 100} ], 
  {k1, 0, 10}, {k2, 0, 10} ]

Answer 1

It can be done like this,

x[t_, k1_, k2_] := 
  1 - (-1 + k2*E^(k1*t + k1))/(-1 + k1*E^(k1*t + k1) + 
      k2*E^(k1*t + k1));
u[t_, k1_, 
   k2_] := (-1 + k2*E^(k1*t + k1))/(-1 + E^(k1*t + k1)*k1 + 
      E^(k1 t  C[1] + k1  C[1] C[2])*k2) /. {C[1] -> 10, C[2] -> 10};
Manipulate[
 Plot[{x[t, k1, k2], u[t, k1, k2]}, {t, 0, 100}], {k1, 0, 10}, {k2, 0,
   10}]