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thils
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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 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}]

enter image description here

First plot shown here.

thils
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