This is an initial attempt to improve your answer. First eliminate errors in the first three lines, and focus on a small `t` up to 1.2. Beyond that there is a singularity/stiff system. This is for the small `t` range!   
    
         Clear[x];
         r = 1; 
        sol = NDSolve[{Derivative[1][x][t] - 1 - r*x[t] - x[t]^2 == 0, 
           x[0] == 0}, x, {t, 0, 1.2}]
        Plot[Evaluate[x[t] /. sol], {t, 0, 1.2}]
        ParametricPlot[Evaluate[{x[t], Derivative[1][x][t]} /. sol], {t, 0, 1.2}]

[![enter image description here][1]][1]

First plot shown here.  


Further to the singularity issue, one can explore the sensitivity of parameters for this specific differential equation using

    Clear[x, r, s]; 
    sol = ParametricNDSolve[{Derivative[1][x][t] - s - r*x[t] == x[t]^2, 
       x[0] == 0}, x, {t, 0, 5}, {r, s}]
    
    Plot[Evaluate[Table[x[r, 0.02][t] /. sol, {r, 0.1, 0.6, 0.02}]], {t, 
      0, 5}, PlotRange -> All]
    
    Plot[Evaluate[Table[x[0.2, s][t] /. sol, {s, 0.01, 0.06, 0.01}]], {t, 
      0, 5}, PlotRange -> All]

The plot (s fixed at 0.02) show how quickly the curve shoots up even for smaller `r` values

[![enter image description here][2]][2]


  [1]: https://i.sstatic.net/KTdjb.png
  [2]: https://i.sstatic.net/5oW3R.png