I used the original:
y = x' and y' = -ibx -c
There is no a.
I'm using Mathematica, not W|A. I figured if it could be worked out in M, W|A could be tried. Here is the code I used (not cleaned up):
{xx, yy} =
DSolveValue[{y'[t] == -I b x[t] - c, x'[t] == y[t],
x[0] == Subscript[\[FormalX], 0],
y[0] == Subscript[\[FormalY], 0]}, {x[t], y[t]}, t] /.
Subscript[a_, b_] :> a /. {\[FormalX] -> x, \[FormalY] -> y}
Block[{a, b, c, x, y, t1 = 0, t2 = 2},
a = 1;
b = 1;
c = 1;
Show[
With[{sols =
Flatten[Table[
Evaluate@{xx, yy}, {x, -4., 4., 1./1}, {y, -4., 4., 1./1}], 1]},
{Table[
ParametricPlot3D[
Evaluate@Table[
Block[{xx, yy, p}, {xx, yy} = s; p = ReleaseHold@param;
If[! FreeQ[p, x | y], Print[p]];
p
],
{s, sols}],
{t, t1, t2},
PlotStyle ->
If[MatchQ[param, _[{Except[0] ..}]], Thick, Thin]],
{param, {(*Hold@{Re@xx,0,Im@xx},Hold@{0,Re@yy,Im@yy},*)
Hold@{Re@xx, Re@yy, 0.5 Im@xx + 0.5 Im@yy}}}]
}
],
Graphics3D[{
Opacity[0.3],
(*Line@Table[{{Re@xx,0,Im@xx},{Re@xx,Re@yy,0.5Im@xx+0.5Im@yy},{0,
Re@yy,Im@yy}},{t,t1,t2,1./2}],*)
InfinitePlane[{0, 0, 0}, {{1, 0, 0}, {0, 0, 1}}],
InfinitePlane[{0, 0, 0}, {{0, 1, 0}, {0, 0, 1}}]
}],
BoxRatios -> {1, 1, 1}, PlotRange -> 10,
AxesLabel -> {Re[x], Re[y], (Im[x] + Im[y])/2}
]
]