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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}]

First plot shown here.

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}]

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

This is an initial attempt to improve your answer. First eliminate errors in the first three lines, and focus on a 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, 3}]
Plot[Evaluate[x[t] /. sol], {t, 0, 3}]
ParametricPlot[Evaluate[{x[t], Derivative[1][x][t]} /. sol], {t, 0, 3}]

First plot shown here.

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}]

First plot shown here.

This is an initial attempt to improve your answer. First eliminate errors in the first three lines, and focus on a 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}]
Plot[Evaluate[x[t] /. sol], {t, 0, 3}]
ParametricPlot[Evaluate[{x[t], Derivative[1][x][t]} /. sol], {t, 0, 3}]

First plot shown here.

This is an initial attempt to improve your answer. First eliminate errors in the first three lines, and focus on a 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, 3}]
Plot[Evaluate[x[t] /. sol], {t, 0, 3}]
ParametricPlot[Evaluate[{x[t], Derivative[1][x][t]} /. sol], {t, 0, 3}]

First plot shown here.