5
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I have the next differential equation 

sol = ParametricNDSolve[{y'[t] == a y[t], y[0] == 1}, y, {t, 0, 10}, {a}]

And a Contour Plot of this equation

 ContourPlot[y[a][x] /. sol, {x, 0, 0.1}, {a, 0, 4},
   PlotLegends -> BarLegend[Automatic, 
    LegendMarkerSize -> 180,   LegendFunction -> "Frame", LegendMargins -> 5,   
    LegendLabel -> "y[a][x]"], Frame -> True,  FrameLabel -> {{"a", ""}, {"x", ""}}, 
     BaseStyle -> {FontWeight -> "Bold", FontSize -> 14}]

With this code, I obtain the next image

enter image description here

I would like to mark the line of constant value $1.5$. To mark this line I click on the line, but I would like to obtain something more "elegant" enter image description here

EDIT

There is a way of isolate that specific line? I mean getting something like this:

enter image description here

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5
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Clear["Global`*"]

sol = ParametricNDSolve[{y'[t] == a y[t], y[0] == 1}, y, {t, 0, 10}, {a}];

Show[
 ContourPlot[y[a][x] /. sol, {x, 0, 0.1}, {a, 0, 4},
  PlotLegends -> BarLegend[Automatic,
    LegendMarkerSize -> 180,
    LegendFunction -> "Frame",
    LegendMargins -> 5,
    LegendLabel -> "y[a][x]"],
  Frame -> True,
  FrameLabel -> {{"a", ""}, {"x", ""}},
  BaseStyle -> {FontWeight -> "Bold", FontSize -> 14}],
 ContourPlot[y[a][x] /. sol, {x, 0, 0.1}, {a, 0, 4},
  Contours -> {1.15},
  ContourStyle -> Directive[Thick, White],
  ContourShading -> None]]

enter image description here

Or

ContourPlot[y[a][x] /. sol, {x, 0, 0.1}, {a, 0, 4},
 PlotLegends -> BarLegend[Automatic,
   LegendMarkerSize -> 180,
   LegendFunction -> "Frame",
   LegendMargins -> 5,
   LegendLabel -> "y[a][x]"],
 Frame -> True,
 FrameLabel -> {{"a", ""}, {"x", ""}},
 BaseStyle -> {FontWeight -> "Bold", FontSize -> 14},
 Contours -> Range[1.05, 1.45, 0.05],
 ContourStyle -> ReplacePart[
   Array[Black, 9],
   3 -> Directive[Thick, Opacity[1, White]]]]

enter image description here

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1
  • $\begingroup$ I think that your answer, solve both of the problems, I mean the original question and the edit of the question, thank you. $\endgroup$ – No name May 18 '20 at 17:57
3
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How about:

  sol = ParametricNDSolve[{y'[t] == a y[t], y[0] == 1}, 
   y, {t, 0, 10}, {a}];
ContourPlot[y[a][x] /. sol, {x, 0, 0.1}, {a, 0, 4}, Frame -> True, 
 FrameLabel -> {{"a", ""}, {"x", ""}}, 
 BaseStyle -> {FontWeight -> "Bold", FontSize -> 14},
 Contours -> {1.15}, ContourStyle -> Directive[Thick, Red], 
 ContourShading -> None]

enter image description here

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2
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Woudl this work?

ContourPlot[
  y[a][x] /. sol, {x, 0, 0.1}, {a, 0, 4},
  PlotLegends -> 
   BarLegend[Automatic, LegendMarkerSize -> 180, 
    LegendFunction -> "Frame", LegendMargins -> 5,
    LegendLabel -> "y[a][x]"],
  Frame -> True, FrameLabel -> {{"a", ""}, {"x", ""}},
  BaseStyle -> {FontWeight -> "Bold", FontSize -> 14},

  Contours -> {{1.15, Thick}}, ContourShading -> None
]

enter image description here

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2
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1. You can use MeshFunctions + Mesh:

ContourPlot[y[a][x] /. sol, {x, 0, 0.1}, {a, 0, 4}, 
 MeshFunctions -> {y[a][x] /. sol /. {x -> #, a -> #2} &}, 
 Mesh -> {{{1.15, Directive[Opacity[1], Thick, White]}}}, 
 PlotLegends -> BarLegend[Automatic, LegendMarkerSize -> 180, 
   LegendFunction -> "Frame", LegendMargins -> 5, 
   LegendLabel -> "y[a][x]"], Frame -> True, 
 FrameLabel -> {{"a", ""}, {"x", ""}}, 
 BaseStyle -> {FontWeight -> "Bold", FontSize -> 14}]

enter image description here

Alternatively, you can use Mesh -> {{1.15}} and add the option MeshStyle -> Directive[White, Thick] to get the same picture.

A slightly more convenient approach is to use ParametricNDSolveValue instead of ParametricNDSolve:

pndsv = ParametricNDSolveValue[{y'[t] == a y[t], y[0] == 1}, y, {t, 0, 10}, {a}];

ContourPlot[pndsv[a][x], {x, 0, 0.1}, {a, 0, 4},  
 MeshFunctions -> {pndsv[#2][#] &}, 
 Mesh -> {{{1.15, Directive[Opacity[1], Thick, White]}}}, 
 PlotLegends -> BarLegend[Automatic, LegendMarkerSize -> 180, 
   LegendFunction -> "Frame", LegendMargins -> 5, 
   LegendLabel -> "y[a][x]"], Frame -> True, 
 FrameLabel -> {{"a", ""}, {"x", ""}}, 
 BaseStyle -> {FontWeight -> "Bold", FontSize -> 14}]

same picture

2. You can post-process ContourPlot output to change the directives for the desired contour line:

cp = ContourPlot[y[a][x] /. sol, {x, 0, 0.1}, {a, 0, 4}, 
   PlotLegends ->  BarLegend[Automatic, LegendMarkerSize -> 180, 
     LegendFunction -> "Frame", LegendMargins -> 5, 
     LegendLabel -> "y[a][x]"], Frame -> True, 
   FrameLabel -> {{"a", ""}, {"x", ""}}, 
   BaseStyle -> {FontWeight -> "Bold", FontSize -> 14}];

cp /.  t : Tooltip[_, 1.15] :> 
    (t /. {Opacity[_] -> Opacity[1], GrayLevel[0] -> Directive[Thick, White]})

enter image description here

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