I have a simple DEQ:

$$y'(t) = y + C$$

for a constant $C$. It turns out that the equilibrium point of this DEQ is $-C$.

I can use the StreamPlot command to plot the direction field for 'any' value of $C$, for example, for $C = 2$:

 StreamPlot[{1, y + 2}, {t, -4, 4}, {y, -8,  4}]

The StreamPlot is:

enter image description here

This StreamPlot would look exactly like this for any value of $C$.

is there some way to show the y-axis as a $C$ instead of $-2$ and to show the other values as $C \pm <\rm{offset}>$. That is, the point $-4$ is shown as $C-2$, the point $-2$ is shown as $C$, the point 0 is shown as $C+2$, etc. In other words, the y-axis values are shown as a function of the general equilibrium point?


You can achieve the desired result using the CustomTicks package, which is part of the LevelScheme package that is available at http://scidraw.nd.edu/levelscheme/

The CustomTicks package lets you specify the desired TickLabelFunction for each axis:


StreamPlot[{1, y + 2}, {t, -4, 4}, {y, -8, 4}, 
  FrameTicks -> {
    {LinTicks[-8, 4, TickLabelFunction -> ("C " <> 
         # == 0, "",
         # < 0,  "- " <> ToString@Abs@#, 
         # > 0,  "+ " <> ToString@#
       ]&@Round[# + 2] &)
    ], Automatic},
    {Automatic, Automatic}

enter image description here

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