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I cannot understand why I cannot reproduce an example given in the NDSolve command help.

Namely I would like to plot the steepest ascent path on the surface $z = x^2-y^2$, starting from the point $(0,-1)$. I try to solve the system of differential equations for the gradient flow

  s = NDSolve[{x'[t] == 2*x[t], y'[t] == -2*y[t], x[0] == 0, 
   y[0] == -1}, {x, y}, {t, 20}]

but when I issue the command, as in the command help

ParametricPlot[Evaluate[{x[t], y[t]} /. s], {t, 0, 20}]

the axes appear, but not the expected plot, a segment from $(-1,0)$ to $(0,0)$, thanks for any hint

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Adding a PlotRange seems to work for me:

ParametricPlot[
 Evaluate[{x[t], y[t]} /. s],
 {t, 0, 20},
 ImageSize -> 400,
 PlotRange -> {-2, 2},
 PlotStyle -> AbsoluteThickness[3]
]

Parametric plot with plot range specified.

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  • $\begingroup$ I would love to understand why Plot Range is not needed in the NDSolve command help.. $\endgroup$
    – Smerdjakov
    May 6, 2019 at 18:07
  • $\begingroup$ @Smerdjakov I don't think PlotRange is needed in general. I think it might be just because the ratio of line width to height is 0:1 and ParametricPlot isn't expecting that? I'm not totally sure though, sorry. $\endgroup$
    – MassDefect
    May 6, 2019 at 18:22

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