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I used the answer herehere and set the independent variable t as first argument. It looks now close to your book

f[t_, x_] := -x
StreamPlot[{1, f[t, x]}, {t, -2, 2}, {x, -.5, .5}, Frame -> False, 
 Axes -> True, AspectRatio -> 1/GoldenRatio]

Mathematica graphics

I used the answer here and set the independent variable t as first argument. It looks now close to your book

f[t_, x_] := -x
StreamPlot[{1, f[t, x]}, {t, -2, 2}, {x, -.5, .5}, Frame -> False, 
 Axes -> True, AspectRatio -> 1/GoldenRatio]

Mathematica graphics

I used the answer here and set the independent variable t as first argument. It looks now close to your book

f[t_, x_] := -x
StreamPlot[{1, f[t, x]}, {t, -2, 2}, {x, -.5, .5}, Frame -> False, 
 Axes -> True, AspectRatio -> 1/GoldenRatio]

Mathematica graphics

1
source | link

I used the answer here and set the independent variable t as first argument. It looks now close to your book

f[t_, x_] := -x
StreamPlot[{1, f[t, x]}, {t, -2, 2}, {x, -.5, .5}, Frame -> False, 
 Axes -> True, AspectRatio -> 1/GoldenRatio]

Mathematica graphics