# NDSolve output - ParametricPlot not plotting

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

## 1 Answer

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]
]


• I would love to understand why Plot Range is not needed in the NDSolve command help.. May 6, 2019 at 18:07
• @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. May 6, 2019 at 18:22