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directionfields from StreamPlot looks different from solution

I don't think I'm using StreamPlot properly.

Consider the following non-autonomous ODE

y'[t] == (t^2) - y[t]

Solutions for various ICs can be viewed by the following.

sol= Table[NDSolve[{y'[t] == (t^2) - y[t], y[0] == y0}, y[t], {t, -4,
4}], {y0, 0, 6, 0.5}];

Plot[Evaluate[y[t] /. sol], {t, -4, 4}, PlotRange -> {{-4, 4}, {-2,

Shouldn't Vector fields be similar to the solutions above? If I plot t
on x-axis vs. t^2-y on y axis...

VectorPlot[{t, (t^2) - y}, {t, -4, 4}, {y, -2, 10}]

StreamPlot[{t, (t^2) - y}, {t, -4, 4}, {y, -2, 10}]

I don't get similar results...

What is the reason for this?

Thanks much in advance


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