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added 1223 characters in body
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Fraccalo
  • 6.1k
  • 15
  • 29

EDIT: for changing the markers, use PointLegend instead of LineLegend combined with LegendMarkers option:

Plot[{d[10, 1, 1, 2, t, 0], , , ,}, {t, 0, 20}, PlotRange -> {0, 5}, 
 LabelStyle -> {FontSize -> 22, FontFamily -> "Times", Black, Bold}, 
 PlotStyle -> {{Darker[Blue], 
    Thickness[0.004]}, {Darker[Blue]}, {Darker[Blue]}, {Darker[
     Blue]}, {Darker[Blue]}}, PlotRangePadding -> 0, 
 LabelStyle -> {FontSize -> 13}, AxesStyle -> Bold, Frame -> True, 
 FrameLabel -> {t[sec], \[ScriptCapitalD][t]}, 
 LabelStyle -> {FontSize -> 13}, AxesStyle -> Bold, 
 FrameStyle -> {{Directive[FontColor -> Darker[Red]], 
    Automatic}, {Directive[FontColor -> Darker[Red]], Automatic}}, 
 PlotLabel -> \[ScriptCapitalD] == 
   Subscript[\[ScriptCapitalD], 
     0] \[Theta][
      t - Subscript[t, 0]]/(1 + 
       Log["1+\[Alpha] t"] (c + Sin[\[Beta] t])), 
PlotLegends -> 
  Placed[PointLegend[{Subscript[\[ScriptCapitalD], 0] == 0, 
     Subscript[t, 0] == 0, "\[Alpha]=1", "c=2", "\[Beta]=1"}, 
    LegendMarkers -> {"\[FilledDiamond]", "\[FilledCircle]", 
      "\[FilledSquare]", "\[CircleTimes]"}, 
    LegendLayout -> "Row"], {0.3, 0.3}]]

EDIT: for changing the markers, use PointLegend instead of LineLegend combined with LegendMarkers option:

Plot[{d[10, 1, 1, 2, t, 0], , , ,}, {t, 0, 20}, PlotRange -> {0, 5}, 
 LabelStyle -> {FontSize -> 22, FontFamily -> "Times", Black, Bold}, 
 PlotStyle -> {{Darker[Blue], 
    Thickness[0.004]}, {Darker[Blue]}, {Darker[Blue]}, {Darker[
     Blue]}, {Darker[Blue]}}, PlotRangePadding -> 0, 
 LabelStyle -> {FontSize -> 13}, AxesStyle -> Bold, Frame -> True, 
 FrameLabel -> {t[sec], \[ScriptCapitalD][t]}, 
 LabelStyle -> {FontSize -> 13}, AxesStyle -> Bold, 
 FrameStyle -> {{Directive[FontColor -> Darker[Red]], 
    Automatic}, {Directive[FontColor -> Darker[Red]], Automatic}}, 
 PlotLabel -> \[ScriptCapitalD] == 
   Subscript[\[ScriptCapitalD], 
     0] \[Theta][
      t - Subscript[t, 0]]/(1 + 
       Log["1+\[Alpha] t"] (c + Sin[\[Beta] t])), 
PlotLegends -> 
  Placed[PointLegend[{Subscript[\[ScriptCapitalD], 0] == 0, 
     Subscript[t, 0] == 0, "\[Alpha]=1", "c=2", "\[Beta]=1"}, 
    LegendMarkers -> {"\[FilledDiamond]", "\[FilledCircle]", 
      "\[FilledSquare]", "\[CircleTimes]"}, 
    LegendLayout -> "Row"], {0.3, 0.3}]]
Source Link
Fraccalo
  • 6.1k
  • 15
  • 29

Try with LineLegend combined with LegendLayout -> "Row":

Plot[{d[10, 1, 1, 2, t, 0], , , ,}, {t, 0, 20}, PlotRange -> {0, 5}, 
 LabelStyle -> {FontSize -> 22, FontFamily -> "Times", Black, Bold}, 
 PlotStyle -> {{Darker[Blue], 
    Thickness[0.004]}, {Darker[Blue]}, {Darker[Blue]}, {Darker[
     Blue]}, {Darker[Blue]}}, PlotRangePadding -> 0, 
 LabelStyle -> {FontSize -> 13}, AxesStyle -> Bold, Frame -> True, 
 FrameLabel -> {t[sec], \[ScriptCapitalD][t]}, 
 LabelStyle -> {FontSize -> 13}, AxesStyle -> Bold, 
 FrameStyle -> {{Directive[FontColor -> Darker[Red]], 
    Automatic}, {Directive[FontColor -> Darker[Red]], Automatic}}, 
 PlotLabel -> \[ScriptCapitalD] == 
   Subscript[\[ScriptCapitalD], 
     0] \[Theta][
      t - Subscript[t, 0]]/(1 + 
       Log["1+\[Alpha] t"] (c + Sin[\[Beta] t])), 
 PlotLegends -> 
  Placed[LineLegend[{Subscript[\[ScriptCapitalD], 0] == 0, 
     Subscript[t, 0] == 0, "\[Alpha]=1", "c=2", "\[Beta]=1"}, 
    LegendLayout -> "Row"], {0.3, 0.3}]
 ]